Deck 6: Analytic Trigonometry

Question 1

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Answer 1

Question 2

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Answer 3

Question 4

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 5

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Question 6

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 7

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 8

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 9

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 10

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 11

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 12

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 13

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 14

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 15

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 16

Find the exact value of the given expression.

A)
B)
C)
D)

Question 17

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

A) 2
B) 0
C) 1
D)
E) -1

Question 18

Find the exact value of the given expression.

A)
B)
C)
D)

Question 19

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 20

Find the exact value of given that and . (Both u and v are in Quadrant II.)

A)
B)
C)
D)
E)

Question 21

Use the figure below to find the exact value of the given trigonometric expression. 5 12
(figure not necessarily to scale)

A)
B)
C)
D)
E)

Question 22

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 23

Find the exact value of the given expression.

A)
B)
C)
D)

Question 24

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 25

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 26

Find the exact value of the given expression.

A)
B)
C)
D)

Question 27

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 28

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Question 29

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 30

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 31

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 32

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 33

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

A) -1
B) 0
C) 1
D)
E) 2

Question 34

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

A)
B)
C)
D)
E)

Question 35

Use the product-to-sum formula to write the given product as a sum or difference.

A)
B)
C)
D)
E)

Question 36

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 37

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Question 38

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 39

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 40

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 41

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 42

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 43

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 44

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

A)
B)
C)
D)
E)

Question 45

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 46

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 47

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 48

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 49

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

A)
B)
C)
D)
E)

Question 50

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 51

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

A) 1
B) 2
C) -1
D) 0
E)

Question 52

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 53

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 54

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 55

Use the figure below to find the exact value of the given trigonometric expression. 5 12
(figure not necessarily to scale)

A)
B)
C)
D)
E)

Question 56

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 57

If , use trigonometric substitution to write as a trigonometric function of F $\theta$ , where .

A)
B)
C)
D)
E)

Question 58

Use the product-to-sum formula to write the given product as a sum or difference.

A)
B)
C)
D)
E)

Question 59

Find the exact value of given that and . (Both u and v are in Quadrant II.)

A)
B)
C)
D)
E)

Question 60

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 61

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 62

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 63

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 64

Find the exact value of the given expression.

A)
B)
C)
D)

Question 65

Find the exact value of given that and . (Both u and v are in Quadrant II.)

A)
B)
C)
D)
E)

Question 66

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

A)
B)
C)
D)
E) 4

Question 67

Use the figure below to find the exact value of the given trigonometric expression. 8 15
(figure not necessarily to scale)

A)
B)
C)
D)
E)

Question 68

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Question 69

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 70

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 71

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 72

Find the exact solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 73

Find the exact value of the given expression using a sum or difference formula.

A)
B)
C)
D)

Question 74

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 75

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 76

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

A)
B)
C)
D)
E)

Question 77

Find the exact value of the given expression.

A)
B)
C)
D)

Question 78

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)

Question 79

Use the product-to-sum formula to write the given product as a sum or difference.

A)
B)
C)
D)
E)

Question 80

If , use trigonometric substitution to write as a trigonometric function of $\theta$ , where .

A)
B)
C)
D)
E)