Download Part I – Multiple Choice 1. Find an expression that completes the

TEST Chapter 6 Practice
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Part I – Multiple Choice
1. Find an expression that completes the fundamental trigonometric identity.
a.  csc x
c. –sin x
b. csc x
csc( x)
d.sin x


2. Find the expression that completes the fundamental trigonometric identity. sec   u 
2

a. sin u
c. –cos u
b. sec u
d. csc u
3. Use the cofunction identity to fill in the blank: sin 13° = cos____°.
a. 23 
b. 167 
c. 87 
d. 77 
4. Factor the expression and use the fundamental identities to simplify.
a.  cos 4 x
c. cos 2 x
b. 1
cos 2 x sin 2 x  cos 2 x
d. tan 2 x
5. Find a fundamental identity that could be used to verify the identity below.
sin 2 x
1
1  cos 2 x
a. even/odd identity
b. quotient identity
c. cofunction identity
6. Find an expression that completes the identity.
a. sin x
b. cos x
c.
d. Pythagorean identity
cos x

1  sin x
1  sec x
sec x
d.
1  sin x
cos x
7. Find an expression that completes the identity. cos2 t (1  sec2 t ) =
a. cos 2 t  1
b. cos 4 t
d. 1  cos 2 t
c. 1
8. Find the exact value of cos105
a.
 2 6
4
b.
2 6
4
c.
6 2
4
d.
6 2
4
1
and sin x > 0, find tan 2x.
12
– 143
143
b.
142
142
9. If cos x =
a.
c.
143
71
d.
– 143
71
10. Express 2sin 7 x cos x as a sum containing only sines or cosines.
a. sin8x  sin 6x
b. sin9x  sin5x
c. sin8x  sin 6x
d. sin9x  sin5x
Part II – Short Answer
11. Use the fundamental trigonometric identities along with the given values to evaluate all six
trigonometric functions of the angle.
2 2


csc      3,sin  
3
2

12. Use the fundamental identities to simplify the trigonometric expression:
csc2 x  1
13. Factor the expression and simplify:
csc x  1
14. Verify the identity: csc4 x  2 csc2 x  1  cot 4 x
cot x
csc x
15. Verify the identity: sin x(tan x  cot x)  sec x
16. Verify the identity:
1
sin x

 sec 2 x
1  sin x 1  sin 2 x
csc2  – cot 2  – cot 
17. Determine if
 sin  – cos  is conditional or is an identity.
csc 
18. Find the exact value of the sine, cosine, and tangent of the angle. (Hint: use the sum and difference formulas)
7
12
19. Given sin u  
3
5
and cos v 
(both u and v are in Quadrant IV), find sin(u  v)
5
13
20. Find the exact value of sin 2x using the double angle formula.
1

cos x  , 0  x 
9
2
21. Use the figure to find the exact value of the trigonometric function. cos

2
6
θ
8
22. Write cos5  cos3 as a product.
Part III – Review
23. Determine the sinθ if θ is an angle in standard position and the point (-5,12) is on the terminal
side of θ.
24. State the amplitude and period of y  5cos 3 x .
25. A construction crew has attached one end of a 100 meter wire cable to the top of a radio tower
that rises vertically from the ground. The other end of the cable is to the ground at a point that is
40 meters from the base of the tower. Assuming that the ground is horizontal, what is the angle
of elevation of the cable? (round to 2 decimal places)