Deck 7: 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

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

A)
B)
C)
D) 3
E)

Answer 2

Question 3

Verify the identity shown below.

Answer 3

Question 4

Rewrite as a single logarithm and then simplify the result.

A)
B)
C)
D)
E)

Question 5

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

A)
B)
C)
D)
E)

Question 6

Verify the identity shown below.

Question 7

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

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

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

A)
B)
C)
D)
E)

Question 10

Which of the following is equivalent to the given expression?

A)
B)
C)
D)
E)

Question 11

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

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

Question 12

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

A)
B)
C)
D)
E)

Question 13

Verify the identity shown below.

Question 14

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

A)
B)
C)
D)
E)

Question 15

If , evaluate the following function.

A)
B)
C)
D)
E)

Question 16

Verify the identity shown below.

Question 17

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 18

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 19

Verify the identity shown below.

Question 20

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

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

A Ferris wheel is built such that the height h (in feet) above the ground of a seat on the wheel at time t (in seconds) can be modeled by . The wheel makes one revolution every 36 seconds and the ride begins when . During the first 36 seconds of the ride, when will a person, who starts at the bottom of the Ferris wheel, be feet above the ground?

A) 10 seconds and 22 seconds
B) 10 seconds and 17 seconds
C) 9 seconds and 27 seconds
D) 9 seconds and 22 seconds
E) 9 seconds and 17 seconds

Question 23

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 24

Write the given expression as the cosine of an angle.

A)
B)
C)
D)
E)

Question 25

Find all solutions of the following equation in the interval .

A)
B)
C)
D)
E)

Question 26

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

A)
B)
C)
D)

Question 27

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

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

Question 28

Find the exact value of the given expression.

A)
B)
C)
D)

Question 29

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 30

Solve the following equation.

A)
B)
C)
D)
E)

Question 31

Solve the following equation.

A)
B)
C)
D)
E)

Question 32

The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by , where q is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 50 feet per second when the ball is hit at an angle of . Round to the nearest foot.

A) 115
B) 154
C) 77
D) 135
E) 38

Question 33

Using the grid provided, sketch the graph of the given function in the interval and then determine the x-intercepts, if any.

A) no x-intercepts
B) (-2,0) and (2,0)
C) (-4,0), (-2,0), (2,0), and (4,0)
D) (-2,0)
E) (-3,0), (-1,0), (1,0), and (3,0)

Question 34

Write the given expression as the tangent of an angle.

A)
B)
C)
D)
E)

Question 35

Find the exact value of the given expression.

A)
B)
C)
D)

Question 36

Solve the following equation.

A)
B)
C)
D)
E)

Question 37

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) March through September
B) April through August
C) March through August
D) August through April
E) May through September

Question 38

Write the given expression as the sine of an angle.

A)
B)
C)
D)
E)

Question 39

Solve the multiple-angle equation.

A)
B)
C)
D)
E)

Question 40

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

A)
B)
C)
D)

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

A)
B)
C)
D)
E)

Question 44

Simplify the given expression algebraically.

A)
B)
C)
D)
E) 1

Question 45

Find the exact value of the given expression.

A)
B)
C)
D)
E)

Question 46

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

A)
B)
C)
D)
E)

Question 47

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

A)
B)
C)
D)
E)

Question 48

Verify the given identity.

Question 49

Use a double angle formula to rewrite the given expression.

A)
B)
C)
D)
E)

Question 50

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

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

Question 51

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

A)
B)
C)
D)
E)

Question 52

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

A)
B)
C)
D)
E)

Question 53

Use the half-angle formula to simplify 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

Simplify the given expression algebraically.

A)
B)
C)
D) 1
E)

Question 56

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 57

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

A)
B)
C)
D)
E)

Question 58

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

A)
B)
C)
D)
E)

Question 59

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)

Question 60

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

A)
B)
C)
D)
E)

Question 61

Find all solutions of the given equation in the interval .

A)
B)
C)
D)
E)

Question 62

The range of a projectile fired at an angle q with the horizontal and with an initial velocity of feet per second is where r is measured in feet. A golfer strikes a golf ball at 120 feet per second. Ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (Round answer to nearest angle.)

A) 18 $\degree$
B) 14 $\degree$
C) 20 $\degree$
D) 5 $\degree$
E) 9 $\degree$