Tài liệu Chuyên đề lượng giác toán 10 trần tài full

TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC PHẦN V: BIẾN ĐỔI LƯỢNG GIÁC A – HỆ THỨC LƯỢNG GIÁC CƠ BẢN  tan   sin  . cos   cot    tan .cot   1 .  sin 2   cos2   1 .  1  tan2   cos  . sin  1 . cos2   1  cot2   1 . sin2  BÀI TẬP ÁP DỤNG Bài 1. Chứng minh các đẳng thức sau 1/ cos2 x  sin2 x  1  2 sin2 x . 2/ 2 cos2 x  1  1  2 sin2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/ 3  4 sin2 x  4 cos2 x  1 . 4/ sin x cot x  cos x tan x  sin x  cos x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ sin 4 x  cos 4 x  1  2 sin 2 x cos2 x . 6/ cos4 x  sin4 x  cos2 x  sin2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ 4 cos2 x  3  1  2 sin x 1  2 sin x  . 8/ 1  cos xsin 2  x  cos x  cos2 x  sin2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 1 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC ................................................................................................................................................... ................................................................................................................................................... 9/ sin4 x  cos4 x  1  2cos2 x  2sin2 x 1 . 10/ sin 3 x cos x  sin x cos 3 x  sin x cos x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 11/ tan2 x  sin2 x  tan2 x sin2 x . 12/ cot2 x  cos2 x  cot2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 2. Chứng minh các đẳng thức sau 1/ tan x  cot x  1 . sin x cos x 2/ 1  cos x sin x  . sin x 1  cos x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/ 1 1   1. 1  tan x 1  cot x 4/    1  1  1  1   tan2 x  0 .         cos x  cos x   ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ 1  sin2 x  1  2 tan2 x . 2 1  sin x 6/ tan x tan y  tan x  tan y . cot x  cot y ................................................................................................................................................... 2 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ 1  cot4 x  2 1  . 2 sin x sin 4 x 8/ tan x  cos x 1  . 1  sin x cos x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 9/ 1 1  cos x1  cot x  1  cos x . 2 10/ 1  cos x 1  cos x 4 cot x   . 1  cos x 1  cos x sin x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 11/ sin x 1  cos x 2   . 1  cos x sin x sin x 12/ sin x  cos x  1 cos x  . sin x  cos x  1 1  sin x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... sin2 x  2 cos x  1 cos x  13/ . 2 1  cos x 2  cos x  cos x 14/ sin x  cos x  1 2 cos x  . 1  cos x sin x  cos x  1 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 3. Chứng minh các đẳng thức sau ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 3 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG 1/ BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC sin 6 x  cos6 x  1  3 sin2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 2/    sin 6 x  cos6 x  sin2 x  cos2 x 1  sin2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/   2 sin 8 x  cos 8 x  1  2 sin2 x cos 2 x  2 sin 4 x cos 4 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 4/    sin 8 x  cos8 x  sin2 x  cos2 x 1  2 sin2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 4. Chứng minh các đẳng thức sau 1/ 1  sin x  cos x  tan x  1  cos x1  tan x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 2/ 1  tan x1  cot x sin x cos x  1  2 sin x cos x . ................................................................................................................................................... 4 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/ 1  tan x cos 2 x  1  cot x  sin 2 x  sin x  cos x  . 2 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 4/ sin 2 x tan x  cos2 x cot x  2 sin x cos x  tan x  cot x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ sin 2 x tan 2 x  4 sin2 x  tan 2 x  3 cos2 x  3 . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 5. Chứng minh các đẳng thức sau 1/ sin2   cos2  tan   1  . 1  2 sin  cos  tan   1 2/ tan2   sin2   tan 6  . 2 2 cot   cos  ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/ cos2  sin2    1  sin  cos  . 1  tan  1  cot  4/ tan   sin  1  . 3 sin  cos  1  cos  ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 5 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ 1  tan2   cot2   2 . 2 2 sin  cos  6/ 1 3 tan2   tan2    1. cos2  cos2  ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ tan2   tan2  sin2   sin 2  .  tan2  tan2  sin2  sin2  8/ 2    1  cos   1  cos     1  2 cot  .  sin   sin2    ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 9/ 1 1  cos  1  cot   1  cos  . 2 10/ 1  tan   tan2   tan3   sin   cos  . cos3  ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 11/ sin  cos  1  cot2    . sin   cos  cos   sin 1  cot2  12/ tan2  1  cot2  1  tan4  .  . 1  tan2  cot2  tan2   cot2  ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 6 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG 2  1  sin  1  sin       4 tan2  . 13/       1  sin  1  sin      BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 2  1  cos  1  cos       4 cot2  . 14/       1  cos  1  cos      ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 6. Rút gọn các biểu thức sau 1/ P1  sin 4   sin2  cos2  . 2/ P2  sin 4   cos4   cos2  . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 3/ P3  sin2   sin2  cot2  . 4/ P4  cos2   cos2  cot2  . ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................   5/ P5  1  sin2  cot2   1  cot2  . 6/ P  sin2  tan  cos2  cot  2sin cos  . 6 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ P7  2 cos2   1 . sin   cos  8/ P8  1  cos  2 sin   1 . 1  cos  ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 9/ P9  cot   cot  . tan   tan  10/ P10  tan   cos  . 1  sin  ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 7 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 11/ P11  sin x  tan x  sin x cot x . tan x 12/ P12  cos x tan x sin2 x  cot x cos x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 13/ P13  cos2 x  cot2 x 2 2 sin x  tan x 14/ P14  . 1  sin2 x cos2 x 2 cos x  cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... sin3 x  sin x cos2 x  cos x 15/ P15  . 1  2 sin x cos x 2 16/ P16 sin x  cos x  1 tan x  sin x cos x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 17/ P17  sin2 x  sin2 x tan2 x 2 2 2 cos x  cos x tan x . 18/ P18  cot2 x  cos2 x 2 cot x  1  cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 8 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG 19/ P19  cos2 x  sin2 y 2 2 sin x sin y  cot2 x cot2 y . BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 20/ P20  1 sin x cos x cot x   . sin x 1  cot x 1  tan x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 21/ P21   1  cos x 1  sin x 1  1  cotx  1  .      tan x  cotx . 22/ P22  1  cotx        sin x cos x sin x  sin x   ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 23/ P  1  tanx cos2 x 1  cotx sin2 x . 23 24/ P  24    , 0  x  .     2 2 2  sinx  cot x  cos x 1 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 7. Biến đổi các biểu thức sau thành tích số 1/ A  2 cos2 x  1 . ................................................................................................................................................... 2/ B  3  4 sin2 x . ................................................................................................................................................... 3/ C  sin x cos x  cos2 x  1 . ................................................................................................................................................... 4/ D  sin2 x  sin x cos x  1 . ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 9 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG 5/ BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC E  1  sin x  cos x  tan x . ................................................................................................................................................... 6/ F  tan x  cot x  sin x  cos x . ................................................................................................................................................... 7/ G  cos x tan2 x  1  cos x  . ................................................................................................................................................... 8/   H  3  4 cos2 x  sin x 2 sin x  1 . ................................................................................................................................................... ................................................................................................................................................... 9/ I  sin2 x  3 cos2 x  6 cos x  2 sin x . ................................................................................................................................................... ................................................................................................................................................... 10/ J  cos3 x  sin3 x  sin x  cos x . ................................................................................................................................................... ................................................................................................................................................... 11/ K  cos3 x  cos2 x  2 sin x  2 . ................................................................................................................................................... ................................................................................................................................................... 12/ L  cos2 x  sin3 x  cos x . ................................................................................................................................................... 13/ M  1  cos x  cos2 x  sin x 1  cos x  . ................................................................................................................................................... 14/ N  2 cos3 x  2 cos2 x  sin x  1 . ................................................................................................................................................... 15/ O  cos3 x  sin3 x  2 sin2 x  1 . ................................................................................................................................................... 16/ P  2 sin x  12 cos x  2 sin x  1  3  4 cos2 x . ................................................................................................................................................... 10 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 17/ Q  2 cos x  1sin x  cos x   1 . ................................................................................................................................................... 18/ R  4 sin3 x  3 cos3 x  3 sin x  sin2 x cos x . ................................................................................................................................................... ................................................................................................................................................... 19/ S  1  sin x  tan2 x  1  cos x . ................................................................................................................................................... 20/ T  2  5 sin x  3 1  sin x  tan2 x . ................................................................................................................................................... 21/ U  2 sin x cos x  2 sin2 x  3 sin x  cos x  1 . ...................................................................................................................................................   22/ V  tan x  3 cot x  4 sin x  3 cos x . ................................................................................................................................................... ................................................................................................................................................... 23/ X  3 sin x  2 cos x  3 tan x  2 . ................................................................................................................................................... 24/ Y  2  tan x  sin x   3 cot x  cos x   5 . ................................................................................................................................................... 25/ Z  3 cot x  cos x  5 tan x  sin x  2 . ................................................................................................................................................... ................................................................................................................................................... Bài 8. Chứng minh các biểu thức sau không phụ thuộc vào biến x 1/ A  cos4 x  sin4 x  2 sin2 x . ................................................................................................................................................... ................................................................................................................................................... 2/ B  sin4 x  sin2 x cos2 x  cos2 x . ................................................................................................................................................... ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 11 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG 3/ BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC C  cos4 x  sin2 x cos2 x  sin2 x . ................................................................................................................................................... ................................................................................................................................................... 4/     D  cos4 x 2 cos2 x  3  sin 4 x 2 sin2 x  3 . ................................................................................................................................................... ................................................................................................................................................... 5/ E  sin6 x  cos6 x  2 sin4 x  cos4 x  sin2 x . ................................................................................................................................................... ................................................................................................................................................... 6/ F  sin x. 1 1  , 1  cos x 1  cos x  0  x      .    4 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ G  sin 4 x  4 cos2 x  cos 4 x  4 sin2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 8/ H  cos2 x cot2 x  5 cos2 x  cot2 x  4 sin2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 9/ I  1  cot x  sin 3 x  1  tan x cos3 x  sin x  cos x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................    10/ J  sin4 x  cos 4 x  1 tan2 x  cot2 x  2 . 12 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................     11/ K  3 sin8 x  cos 8 x  4 cos6 x  2 sin 6 x  6 sin 4 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................     12/ L  sin4 x 1  sin2 x  cos 4 x 1  cos2 x  5 sin 2 x cos2 x  1 . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...................................................................................................................................................    2  13/ M  2 sin4 x  cos4 x  sin2 x cos2 x  sin 8 x  cos8 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 9. Chứng minh các biểu thức sau không phụ thuộc vào biến x 1/ A 2 cot x  1  . tan x  1 cot x  1 ................................................................................................................................................... ................................................................................................................................................... 2/ B  1  tan2 x 2 4 tan x  2  1 2 4 sin x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 13 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG 3/ C BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 1  tan2 x  1  tan2 x 1  cot2 x . tan x    ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 1  cot x D 2 2 4/ cot2 x  1 sin2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ E 1  sin6 x cos6 x  3 tan2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 6/ F tan2 x  cos2 x sin2 x  cot2 x  sin2 x cos2 x . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ G cot2 x  cos2 x 2 cot x  sin x cos x . cot x ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 8/ H 14 | THBTN – CA sin4 x  cos4 x  1 sin6 x  cos6 x . FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 15 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC B – ĐƯỜNG TRÒN LƯỢNG GIÁC – CUNG GÓC LƯỢNG GIÁC CUNG LIÊN KẾT 1. Đường tròn lượng giác và dấu góc lượng giác sinx Cung 1 I II III IV + + – – + – – + + – + – + phần tư π – + – 2 Giá trị LG (II) (I) π 0 1 2π O -1 cosx (IV) (III) 3π 2 (Nhất cả – Nhì sin – Tam tan – Tứ cos) -1 2.Cung liên kết Cung đối nhau Cung bù nhau cos(a)  cos a sin(   a)  sin a   sin   a   cos a 2  sin(a)   sin a cos(   a)   cos a   cos   a   sin a 2  tan(a)   tan a tan(   a)   tan a   tan   a   cot a 2  cot(a)   cot a cot(   a)   cot a   cot   a  tan a    2    Cung hơn kém  Cung phụ nhau Cung hơn kém sin(   a)   sin a   cos   a    sin a 2   tan(   a)  tan a   tan   a    cot a 2   cot(   a)  cot a 16 | THBTN – CA   sin   a   cos a 2  cos(   a)   cos a  2   cot   a    tan a 2  FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC BÀI TẬP ÁP DỤNG MỐI LIÊN HỆ GIỮA ĐƠN VỊ ĐỘ VÀ RADIAN Bài 10. Đổi số đo các cung sau ra độ, phút, giây: 2 3 5  7 13 3 15  , , , , , ,  , 2, , . 3 4 9 5 3 3 4 7 15 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 11. Đổi số đo các góc sau ra radian rad : 900, 360, 150 , 720 , 2700, 2400, 5400, 7500 , 210 . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 12. Đổi số đo độ của các cung tròn sau thành số đo radian (chính xác đến phần nghìn): 21030 ', 75054 ', 12036 ' , 15030 ',  105045 ' 30 '', 27 038 ' 49 '' . ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 13. Điền các giá trị thích hợp vào ô trống 00 150 300 450 600 750 900 1200 1500 1800  16  8  6 5 12  2 2 3 3 4 5 6  4 3 ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 17 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG Radian 7 4  12 BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 5 6 Độ  2 2 3 3 4 1350  500 8100 TÍNH ĐỘ DÀI CUNG TRÒN Bài 14. Một đường tròn có bán kính 10 cm  . Tính độ dài các cung có số đo là 2  3 7 13 3 3 , , , , ,  2, , 450, rad, 75 0 . 3 18 5 3 6 4 2 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 15. Kim giờ của đồng hồ dài 7 cm  , kim phút dài 10 cm  . Tính quãng đường kim phút, kim giờ đi được trong 30 phút. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 16. Bánh xe có đường kính (tính cả lốp) là 55 cm . Nếu xe chạy với vận tốc 40 km /h thì trong một giây bánh xe quay được bao nhiều vòng ? ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 17. Kim phút và kim giờ của đồng hồ lớn nhà Bưu Điện Hà Nội theo thứ tự dài 1, 75 m  và 1, 26 m  . Hỏi trong 15 phút, mũi kim phút và mũi kim giờ vạch trên cung tròn có độ dài bằng bao nhiêu mét ? ................................................................................................................................................... 18 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... BIỂU DIỄN NGỌN CUNG LƯỢNG GIÁC Bài 18. Biểu diễn các góc sau lên đường tròn lượng giác gốc A: 300 ,  450, 1200,  1200, 3300, 6300, 7500 ,  12500, 7 4 15 2010 ,  ,  750 0, 11250 , , . 4 3 2 4 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 19.    Xác định điểm cuối của cung có số đo: k2, k, k , k , k , k   . 2 3 4 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 20. Xác định điểm ngọn của các họ nghiệm sau đây trên đường tròn lượng giác với k  . 1/ x  k . 2/ x    k2 . 2 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 19 | THBTN TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG 3/ x  4k . BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 4/ x    k . 3 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 5/ x     k2 . 6 6/ x     k . 4 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 7/ x  k . 3 8/ x   k2  . 3 3 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 9/ x   k3  . 4 4 10/ x   k  . 6 3 ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Bài 21.  k   Cho hai điểm M và N sao cho sđ AM  và sđ AN  với k   . Tìm k   để: 6 798 1/ M trùng với N. 2/ M đối xứng với N qua tâm O. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... 20 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341