Deck 6: Analytic Trigonometry

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)

Answer 1

Question 2

Find the exact value of the given expression.

A)
B)
C)
D)

Answer 2

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A)
B)
C)
D)
E)

Question 5

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 6

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 7

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

A)
B)
C)
D)

Question 8

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 9

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 10

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

A)
B)
C)
D)

Question 11

Find the exact value of the given expression.

A)
B)
C)
D)

Question 12

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 13

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 14

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

A)
B)
C)
D)
E)

Question 15

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 16

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 17

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 18

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

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 21

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 22

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 23

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

A)
B)
C)
D)

Question 24

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

A)
B)
C)
D)
E)

Question 25

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

A)
B)
C)
D)
E)

Question 26

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 27

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

A)
B)
C)
D)
E)

Question 28

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

A)
B)
C)
D)
E)

Question 29

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 30

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

A)
B)
C)
D)
E)

Question 31

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 32

Find the exact value of the given expression.

A)
B)
C)
D)

Question 33

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 34

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 35

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 36

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

A)
B)
C)
D)

Question 37

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 38

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

A)
B)
C)
D)
E)

Question 39

Find the exact value of the given expression.

A)
B)
C)
D)

Question 40

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 41

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 42

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 43

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

A)
B)
C)
D)
E)

Question 44

Find the exact solutions 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

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 47

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 48

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

A)
B)
C)
D)
E)

Question 49

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

A)
B)
C)
D)
E)

Question 50

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

A)
B)
C)
D)
E)

Question 51

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 52

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 53

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

A)
B)
C)
D)
E)

Question 54

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 55

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 56

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 57

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 58

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 59

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 60

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

A)
B)
C)
D)
E)

Question 61

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

A)
B)
C)
D)
E)

Question 62

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 63

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

A)
B)
C)
D)
E)

Question 64

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 65

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

A)
B)
C)
D)
E)

Question 66

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

A)
B)
C)
D)

Question 67

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 68

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 69

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 70

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

A)
B)
C)
D)
E)

Question 71

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

A)
B)
C)
D)
E)

Question 72

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

A)
B)
C)
D)
E)

Question 73

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

A)
B)
C)
D)
E) 4

Question 74

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 75

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

A)
B)
C)
D)
E)

Question 76

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

A)
B)
C)
D)
E)

Question 77

Find the exact value of the given expression.

A)
B)
C)
D)

Question 78

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

A)
B)
C)
D)

Question 79

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 80

Find the exact value of the given expression.

A)
B)
C)
D)