# A- LEVEL TOPIC REVIEW

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```					                               A– LEVEL TOPIC REVIEW

unit C3                                                                            trigonometry

1. Write down the exact values of:
a)   cos 1 
3                   b)    sec 1 
3                    c)     cot 1 
6

d)   cosec(45)             e)    sec225                  f)     cot 300            (6 marks)

2. Solve these equations for 0  x  360 :
a) cosec x  2                                  b)   cot 2x  1
2
c) sec( x  30)                              d)   cot x  cosec x  sin x         (10 marks)
3

3. Sketch, on the same axes, the graphs of y  sin x and y  cosec x for   x  2 . (3 marks)

4. Given that A is obtuse and B is acute, with sin A  5 and cos B  12 , find the exact values of:
4
13

a)   sin( A  B)             b)    cos( A  B)              c)     tan( A  B)         (7 marks)

5. a) Express 3cos x  4sin x in the form R cos( x   ) , where 0    1  .
2
(2 marks)
b) Write down the maximum value of 3cos x  4sin x .                                   (1 mark)
1
c) Write down the smallest positive value of                     .                     (1 mark)
3cos x  4sin x  2
d) Solve the equation 3cos x  4sin x  1 for 0  x  2 .                           (3 marks)

6. Solve these equations for 0  x  360 :
a)   sin x  cos 1 x
2                               b)   tan x  tan 1 x  0
2                    (7 marks)

7. Prove the following identities. You may assume the formulas for sin 2x and cos 2x .
1  cos 2 x
a) tan x  cot x  2cosec2x                b)               tan x
sin 2 x
c)   cos3x  4cos3 x  3cos x                                                         (10 marks)

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