Xi Trigonometry Assignment

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