Deck 11: Analytic Trigonometry

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

Which of the following is not an identity?

A)
B)
C)
D)
E)

Answer 2

Question 3

Verify the identity shown below.

Answer 3

Question 4

Verify the identity shown below.

Question 5

Verify the identity shown below.

Question 6

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

A)
B)
C)
D)
E)

Question 7

If , evaluate the function below.

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

A)
B)
C)
D)
E)

Question 10

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 11

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

A)
B)
C)
D)
E)

Question 12

Which of the following is equivalent to the expression below?

A)
B)
C)
D)
E)

Question 13

Verify the identity shown below.

Question 14

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

A)
B)
C)
D)
E)

Question 15

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

A)
B)
C)
D)
E)

Question 16

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 17

Verify the identity shown below.

Question 18

The rate of change of the function is given by the expression ^.Which of the following is its simplification?

A)
B)
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

If , evaluate the following function.

A)
B)
C)
D)
E)

Question 21

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval .

A)
B)
C)
D)
E)solution does not exist

Question 22

Which of the following is a solution to the given equation?

A)
B)
C)
D)
E)

Question 23

Solve the following equation.

A)
B)
C)
D)
E)

Question 24

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

A)
B)
C)
D)

Question 25

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 26

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)
B)
C)
D)
E)

Question 27

Using a graphing utility, graph each side of the equation to determine whether the equation is an identity.

A)identity
B)not an identity

Question 28

Verify the identity shown below.

Question 29

Find all solutions of the following equation in the interval .

A)
B)
C)
D)
E)

Question 30

Solve the following equation.

A)
B)
C)
D)
E)

Question 31

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 32

Find all solutions of the following equation in the interval .

A)
B)
C)
D)
E)

Question 33

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 34

Using a graphing utility, graph each side of the equation to determine whether the equation is an identity.

A)identity
B)not an identity

Question 35

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 36

Solve the following equation.

A)
B)
C)
D)
E)

Question 37

Solve the multiple-angle equation in the interval .

A)
B)
C)
D)
E)

Question 38

Verify the identity shown below.

Question 39

Verify the identity shown below.

Question 40

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with corresponding to January. Determine the months when sales exceed units at any time during the month.

A)July through May
B)May through July
C)June through August
D)April through August
E)April through July

Question 41

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

A)
B)
C)
D)
E)

Question 42

Write the given expression as an algebraic expression.

A)
B)
C)
D)
E)

Question 43

Use the figure below to determine the exact value of the given function.

A)
B)
C)
D)
E)

Question 44

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

A)
B)
C)
D)
E)

Question 45

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 46

Simplify the given expression algebraically.

A)
B)
C)
D)
E)

Question 47

Use a double-angle formula to find the exact value of when .

A)
B)
C)
D)
E)

Question 48

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 49

Find the exact value of the given expression.

A)
B)
C)
D)

Question 50

Find the exact value of the given expression.

A)
B)
C)
D)

Question 51

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

A)
B)
C)
D)
E)

Question 52

Use a double-angle formula to find the exact value of when .

A)
B)
C)
D)
E)

Question 53

Use a double angle formula to rewrite the given expression.

A)
B)
C)
D)
E)

Question 54

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

A)
B)
C)
D)
E)

Question 55

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 56

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

A)1
B)-1
C)
D)
E)undefined

Question 57

Simplify the given expression algebraically.

A)
B)
C)
D)
E)

Question 58

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

A)
B)
C)
D)
E)

Question 59

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

A)
B)
C)
D)

Question 60

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 61

Use the sum-to-product formulas to find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 62

Use the figure below to find the exact value of the given trigonometric expression.

A)
B)
C)
D)
E)

Question 63

Use the sum-to-product formulas to write the given expression as a product.

A)
B)
C)
D)
E)

Question 64

Verify the given identity.

Question 65

Use the power-reducing formulas to rewrite the given expression in terms of the first power of the cosine.

A)
B)
C)
D)
E)

Question 66

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

A)
B)
C)
D)
E)

Question 67

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 68

Use the figure below to find the exact value of the given trigonometric expression. 68(figure not necessarily to scale)

A)
B)
C)
D)
E)

Question 69

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

A)
B)
C)
D)
E)

Question 70

Verify the given identity.

Question 71

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 72

Use the half-angle formula to simplify the given expression.

A)
B)
C)
D)
E)

Question 73

The range of a projectile fired at an angle with the horizontal and with an initial velocity of feet per second is where r is measured in feet. A golfer strikes a golfball at 80 feet per second. Ignoring the effects of air resistence, at what angle must the golfer hit the ball so that it travels 110 feet? (Round answer to nearest angle.)

A)
B)
C)
D)
E)