ASSIGNMENT CLASS XI TRIGONOMETRY 1. The larger hand of a big clock is 35 cm long. How many cm does its tip move in 9 minutes? 2. In a rigt angled triangle , the difference between two acute angles is
. Express the angles in degrees. 18
3. The angles of a triangle are in A.P. and the number of degrees in the least to the number of radians in the greatest is 60: . Find the angles in radians. 4. If cot
12 and lies in the second quadrant, find the values of other five trigonometric functions. 5
1 5 3 5. If cot , , and sec , , , find the value of tan . 2 2 3 2 4 12 3 3 6. If cos x , cos y ; x 2 and y 2 , find the values of cos x y and sin x y . 5 13 2 2
3 5 7 7. Prove that (i) cos 2 cos 2 cos 2 cos 2 2 8 8 8 8 8. If tan
3 5 7 (ii) sin 2 sin 2 sin 2 sin 2 2 4 4 4 4
m 1 and tan , show that . 4 m 1 2m 1 (i) cos 200 cos 400 cos800
9. Prove that:
1 8
(ii) sin100 sin 500 sin 60 0 sin 70 0
1 10. Prove that: (i) cos cos cos cos 3 (ii) sin sin 3 3 3 4 11. Prove that:
(i)
sin 8 cos sin 6 cos 3 tan 2 cos 2 cos sin 3 sin 4
(i ) 3sin x
12. Draw the graph of:
(ii ) sin 2 x
(ii)
3 . 16
2 1 sin sin 3 3 4
sin A B 2 sin A sin A B tan A cos A B 2 cos A cos A B
(iii ) cos x
(iv) 3cos 2 x
13. Solve the following trigonometric equations:
(i ) sin 3 x cos 2 x 0
(ii ) 3tan x cot x 5cos ecx
(iv ) sin 2 x sin 4 x sin 6 x 0
(v) cos 3 x cos x cos 4 x cos 2 x
(iii ) 2 tan x cot x 1 0
ANSWERS 1. 33 cm 2. 500 , 400
5.
2 11
(iii ) x n
6.
3.
, , 6 3 2
33 16 , 65 65
3 1 or x m , tan 4 2
4. cos ec
13 5 5 12 13 , tan ,sin , cos ,sec 5 12 13 13 12
2n or x 2 5 10 2m (v) x 2n , or 2 p 1 5 2
13. (i ) x 2n
(ii ) 2n
3