H. Pre-Calc: 7.1 - 7.5 REVIEW, Trigonometry
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Given
and
, find
a.
and
c.
,
b.
____
,
d.
,
2. What basic trigonometric identity would you use to verify that cot x sin x = cos x?
a.
c.
b.
____
____
d.
3. What basic trigonometric identity would you use to verify that
a. sin x = cos x tan x
c.
b.
d.
4. Find sec x if
a.
____
,
?
.
b.
5. Find cos x if sin x cot x = 4.
a. 4
b.
c.
d.
c. 1
d. No Solution
____
6. Find cos x if
.
a. –1
____
____
b. 2
7. Find the exact value of cos 15.
a.
b.
d. 0
c.
d.
8. If  and  are the measures of two first quadrant angles and sin 
find sin (+ ).
a.
____
c. 1
b.
c.
and sin 
d.
9. Which sum or difference identity would you use to verify that sin (90 + ) = cos ?
a. cos ( ) = cos cos + sin sin 
b. sin ( ) = sin cos + cos  sin 
c. sin ( ) = sin cos  cos sin 
d. cos ( ) = cos cos  sin sin 
____ 10. If
a.
and  terminates in the fourth quadrant, find the exact value of tan 2.
b.
c.
____ 11. Use a half-angle identity to find the exact value of tan 105.
a.
c.
b.
d.
d.
,
____ 12. Which double-angle or half-angle identity would you use to verify that
a.
c.
b.
d.
____ 13. Solve
a. 150
for
b. 30
____ 14. Solve
a.
.
c. 60
?
d. 120
for all real values of x.
c.
b.
d.
Short Answer
15. If  is between
and
find
. Enter the missing value in the below answer:
=
16. Find a numerical value of csc x if
17. Find cos x if
.
. Enter the missing value in the following answer:
.
18. Find the exact value of sin 15.
Enter the missing value in the following answer:
19. If  and  are the measures of two first quadrant angles and
20. If
and
, find
.
and q terminates in the third quadrant, find the exact value of sin2q.
Enter the missing value of the following answer:
21. If
and  terminates in the first quadrant, find the exact value of sin 2
22. Solve
choice.
= 0 for
a) 0
f) 120
23. Solve
24. Solve
b) 30
g) 135
for
for
. Choose all the correct answers in alphabetical order by
c) 45
h) 160
.
.
Enter the missing value for the following answer:
d) 60
i) 180
e) 90
Verify the identity. Do not cross the equality.
25. Verify that
.
.
.
.
.
.
.
.
.
.
.|
26. Verify that
.
.
.
.
.
.
.
.
.
.
.|
is an identity.
is an identity.
27. Verify that sin ( + ) = sin  is an identity.
.
.
.
.
.
.
.
.
.
.
.|
28. Verify that
is an identity.
.
.
.
.
.
.
.
.
.
.
.|
29. Verify that cos (270 ) = sin  is an identity.
.
.
.
.
.
.
.
.
.
.
.|
H. Pre-Calc: 7.1 - 7.5 REVIEW, Trigonometry
Answer Section
MULTIPLE CHOICE
1. ANS: A
TOP: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities,
and opposite-angle identities.
2. ANS: B
TOP: Use the basic trigonometric identities to verify other identities.
3. ANS: C
TOP: Use the basic trigonometric identities to verify other identities.
4. ANS: D
TOP: Find the numerical values of trigonometric functions.
5. ANS: D
TOP: Find the numerical values of trigonometric functions.
6. ANS: C
TOP: Find the numerical values of trigonometric functions.
7. ANS: B
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
8. ANS: A
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
9. ANS: B
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
10. ANS: B
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
11. ANS: A
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
12. ANS: D
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
13. ANS: D
TOP: Solve trigonometric equations and inequalities.
14. ANS: D
TOP: Solve trigonometric equations and inequalities.
SHORT ANSWER
15. ANS:
TOP: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities,
and opposite-angle identities.
16. ANS:
TOP: Find the numerical values of trigonometric functions.
17. ANS:
TOP: Find the numerical values of trigonometric functions.
18. ANS:
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
19. ANS:
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
20. ANS:
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
21. ANS:
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
22. ANS:
0, 120, 180
TOP: Solve trigonometric equations and inequalities.
23. ANS:
90
TOP: Solve trigonometric equations and inequalities.
24. ANS:
TOP: Solve trigonometric equations and inequalities.
25. ANS:
TOP: Use the basic trigonometric identities to verify other identities.
26. ANS:
TOP: Use the basic trigonometric identities to verify other identities.
27. ANS:
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.
28. ANS:
TOP: Use the double- and half-angle identities for the sine, cosine, and tangent functions.
29. ANS:
TOP: Use the sum and difference identities for the sine, cosine, and tangent functions.