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BLM 6–7
Chapter 6 Test
Multiple Choice
For 1 to 5, choose the best answer.
cot 2
.
1  cot 2
1. Simplify the expression
A cos2  
C tan2  
B sin2 
D sec2 
2. The value of (sin x cos x)2  sin 2x is
A 1
C 1
B 0
D 2
1  tan 2
3. The expression
is equivalent to
1  tan 2
A cos 2 
C cos2  
B sin 2
D sin2 
4. If you simplify sin (  x)  sin (  x) it is
A 2
C 2
B 0
D not possible
5. Which of the following is not an identity?
A sec   cos   sin  tan 
B 1  cos2   cos2  tan2 
C csc   cos  tan  
cos 
tan 
1  cos2
D cos  
2
2
Short Answer
 5π 
6. Determine the exact value of sin    .
 12 
sin 2 x
7. Given
 1.23.
1  cos x
5
3π
, πθ
, determine the
13
2
π
exact value of sin  θ   .

2
9. If cosθ 
10. What single trigonometric function is
equivalent to
y
y
sin (3 y) cos    cos(3 y)sin   ?
 2
 2
Extended Response
11. Consider the equation
π
sin  x    csc x  1

2
a) Verify the equation is true for x 
π
.
2
b) Is the equation an identity? Explain.
12. Consider the equation
sin2 x  cos4 x  cos2 x  sin4 x.
a) Verify the equation for x  30.
b) Prove the equation is an identity.
13. Consider the equation
tan x  sec x
sin x

.
cot x
1  sin x
a) State the non-permissible values on the
domain 0  x  360.
b) Prove the equation is an identity
algebraically.
14. Solve sin 2x  cos x  0 algebraically for the
domain   x  .
15. Solve csc2 x  4 cot2 x algebraically. State
the general solution in radians.
What is the value of cos x?
8. If 5  7 sin   2 cos2   0 on the domain
90    180, what is the value of ?
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-073887-4
Chapter 6 Test Answers
1. A
3. A
6.
2. C
4. B
 6 
5. D
2
4
7. 0.23
8. 150
9.
5
13
 5y
10. sin  
 2


11. a) Left side  sin  x  

2
  
 sin   
2
2
 sin   
 0
Right side  csc x  1

1
2
 11
 csc
 0
b) No; it is not true for all permissible values of x.
12. a) Left side  sin 2 x  cos 4 x
 sin 2 30  cos 4 30
2
 3
 1
    
 2
 2

4
13
16
Right side  cos 2 x  sin 4 x
 cos 2 30  sin 4 30
2
4
 3
 1
   
 2
 2 

13
16
b) Example:
Left side  sin 2 x  cos 4 x
 sin 2 x  (1  sin 2 x) 2
 sin 2 x  1  2sin 2 x  sin 4 x
 1  sin 2 x  sin 4 x
 cos 2 x  sin 4 x
 Right side
Right side  cos 2 x  sin 4 x
13. a) x  0, 90, 180, 270, 360
b) Example:
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 9780070738874
Left side 
tan x  sec x
cot x
1 
 sin x
 

 cot x
 cos x cos x 
 sin x  1  cos x 
 

 cos x   sin x 
 sin x  1  sin x 
 

 cos x   cos x 



 sin x  1 sin x
2
1  sin x
 sin x  1 sin x
(1  sin x)(1  sin x)
sin x
(1  sin x)
 Right side
sin x
Right side 
1  sin x
  5
,
2 6 6
14.  ,
15.

2
  n,
  n; n  I
3
3
Copyright © 2012, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-073887-4