Prof. Israel N Nwaguru
MATH 1316
CHAPTER 2 - REVIEW
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use fundamental identities to simplify the expression below and then determine which of the
following is not equivalent.
a.
____
b.
c.
d.
e.
2. Use fundamental identities to simplify the expression below and then determine which of the
following is not equivalent.
a.
____
b.
c.
d.
e.
3. Factor; then use fundamental identities to simplify the expression below and determine which of the
following is not equivalent.
a.
____
b.
c.
d.
e.
4. Factor; then use fundamental identities to simplify the expression below and determine which of the
following is not equivalent.
a.
b.
c.
d.
e.
____
5. Multiply; then use fundamental identities to simplify the expression below and determine which of
the following is not equivalent.
a.
____
b.
c.
d.
e.
6. Which of the following is equivalent to the given expression?
a.
____
b.
7. If
c.
d.
as a trigonometric function of ,
, use trigonometric substitution to write
.
where
e.
a.
b.
c.
d.
e.
____
8. If
where
a.
____
9. If
.
b.
c.
____ 10. Rewrite
a.
d.
e.
as a trigonometric function of ,
, use trigonometric substitution to write
where
a.
as a trigonometric function of ,
, use trigonometric substitution to write
.
b.
c.
d.
e.
as a single logarithm and then simplify the result.
b.
c.
d.
e.
____ 11. Which of the following is a solution to the given equation?
a.
b.
c.
d.
e.
____ 12. Which of the following is a solution to the given equation?
a.
b.
c.
____ 13. Solve the following equation.
d.
e.
a.
b.
c.
d.
e.
____ 14. Solve the following equation.
a.
b.
c.
d.
e.
____ 15. Find all solutions of the following equation in the interval
a.
b.
c.
____ 16. Solve the multiple-angle equation.
a.
b.
c.
d.
e.
d.
.
e.
____ 17. Use the Quadratic Formula to solve the given equation on the interval
; then use a graphing
utility to approximate the angle x. Round answers to three decimal places.
a.
e.
b.
c.
d.
____ 18. Use inverse functions where needed to find all solutions (if they exist) of the given equation on the
interval
.
b. solution does not exist
a.
c.
d.
e.
____ 19. Find the exact value of the given expression.
a.
b.
c.
d.
____ 20. Find the exact value of the given expression.
a.
b.
c.
d.
____ 21. Find the exact value of the given expression using a sum or difference formula.
a.
b.
c.
d.
____ 22. Find the exact value of the given expression using a sum or difference formula.
a.
b.
c.
d.
____ 23. Write the given expression as the sine of an angle.
a.
b.
c.
d.
e.
____ 24. Write the given expression as the cosine of an angle.
a.
b.
c.
d.
e.
____ 25. Write the given expression as the tangent of an angle.
a.
b.
c.
d.
e.
____ 26. Find the exact value of the given expression.
a.
b.
c.
d.
____ 27. Find the exact value of
e.
given that
and
. (Both u and v are in
Quadrant II.)
a.
b.
c.
d.
e.
____ 28. Find the exact value of
given that
and
. (Both u and v are in
Quadrant II.)
a.
b.
c.
e.
____ 29. Simplify the given expression algebraically.
a. 1
b.
c.
d.
e.
____ 30. Simplify the given expression algebraically.
d.
a.
b. 1
c.
d.
e.
____ 31. Use the figure below to determine the exact value of the given function.
a.
b.
c.
d.
____ 32. Find the exact solutions of the given equation in the interval
a.
b.
c.
e.
.
d.
e.
____ 33. Use the figure below to find the exact value of the given trigonometric expression.
15
36
(figure not necessarily to scale)
a.
b.
c.
d.
e.
____ 34. Use the figure below to find the exact value of the given trigonometric expression.
a.
b.
c.
d.
e.
____ 35. Use the half-angle formulas to determine the exact value of the given trigonometric expression.
a.
b.
c.
d.
e.
____ 36. Use the product-to-sum formula to write the given product as a sum or difference.
a.
b.
c.
d.
e.
____ 37. Use the sum-to-product formulas to find the exact value of the given expression.
a.
b. –1
c.
d.
Short Answer
38. Verify the identity shown below.
39. Verify the identity shown below.
40. Verify the given identity.
e.
MATH 1316
CHAPTER 2 - REVIEW
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
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25.
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29.
30.
31.
32.
33.
34.
35.
36.
37.
ANS:
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B
C
A
E
A
E
B
E
A
B
A
D
D
D
C
B
E
C
A
C
A
D
A
C
B
C
D
A
C
A
E
E
C
C
A
D
E
SHORT ANSWER
38. ANS:
39. ANS:
40. ANS: