Deck 8: Trigonometric Functions

Question 1

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
cos θ = 0.63

A)
B)
C)
D)

Answer 1

Question 2

Find the exact value without using a calculator.
cot

A)
B)
C)
D)

Answer 2

Question 3

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
tan 0.8

A) 0.0184
B) 1.0265
C) 0.0139
D) 1.0296

Answer 3

1.0296

Question 4

Find the trigonometric ratio by referring to the figure.
tan

A)
B)
C)
D)

Question 5

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
sec

A) 3.8744
B) 2.0627
C) 3.8193
D) 2.0732

Question 6

Find the trigonometric ratio by referring to the figure.
cot

A)
B)
C)
D)

Question 7

Find the exact value without using a calculator.
cos

A)
B)
C)
D)

Question 8

Find the exact value without using a calculator.
csc 60°

A)
B)
C)
D)

Question 9

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
cos

A) 0.8439
B) 0.9732
C) 0.9781
D) 0.8427

Question 10

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
csc

A) 1.0117
B) 1.0154
C) 1.0061
D) 1.0525

Question 11

Find the exact value without using a calculator.
sec

A)
B)
C)
D)

Question 12

Find the trigonometric ratio by referring to the figure.
cos

A)
B)
C)
D)

Question 13

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
tan θ = 7

A)
B)
C)
D)

Question 14

Find the exact value without using a calculator.
tan

A)
B)
C)
D)

Question 15

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
cot

A) 0.1733
B) 1.2739
C) 1.3764
D) 0.1290

Question 16

Find the exact value without using a calculator.
sin

A)
B)
C)
D)

Question 17

Use a calculator set in degree or radian mode, as appropriate, to find the value of each expression to four decimal places.
sin 0.7

A) 0.6426
B) 0.0122
C) 0.0168
D) 0.6442

Question 18

Find the trigonometric ratio by referring to the figure.
csc

A)
B)
C)
D)

Question 19

Find the trigonometric ratio by referring to the figure.
sin

A)
B)
C)
D)

Question 20

Find the trigonometric ratio by referring to the figure.
sec

A)
B)
C)
D)

Question 21

Refer to the figure and use the given information to solve the triangle. Round angles to the nearest degree and side
lengths to one decimal place.
A = = 4.7

A)
B)
C)
D)

Question 22

Provide an appropriate response.
Convert to radian measure. Leave your answer in terms of

A)
B)
C)
D)

Question 23

Provide an appropriate response.
Evaluate cos

A)
B)
C)
D)

Question 24

Refer to the figure and use the given information to solve the triangle. Round angles to the nearest degree and side
lengths to one decimal place.
B =

A)
B)
C)
D)

Question 25

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
sin θ = 0.2

A)
B)
C)
D)

Question 26

Provide an appropriate response.
Find the exact value of sin

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

Question 27

Solve the problem.
An angle above the horizontal is called an angle of elevation, and an angle below the horizontal is called an angle of depression. The pilot of a boat sees the light from a lighthouse at an angle of elevation of 13°. The light is on the shoreline, 350 feet above the dock. How far (to the nearest hundred feet) is the boat from the dock?

A) 1400 feet
B) 1500 feet
C) 2100 feet
D) 1600 feet

Question 28

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
cos θ = 0.9

A)
B)
C)
D)

Question 29

Refer to the figure and use the given information to solve the triangle. Round angles to the nearest degree and side
lengths to one decimal place.
b = 7.5, c = 14.9

A) A = 45, B = 45, C = 90, a = 13.2, b = 7.5, c = 14.9
B) A = 30, B = 60, C = 90, a = 12.6, b = 7.5, c = 14.9
C) A = 60, B = 30, C = 90, a = 12.9, b = 7.5, c = 14.9
D) A = 60, B = 30, C = 90, a = 11.4, b = 7.5, c = 14.9

Question 30

Provide an appropriate response.
Evaluate sin

A)
B)
C)
D)

Question 31

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
sin θ = 0.32

A)
B)
C)
D)

Question 32

Provide an appropriate response.
Convert to radian measure. Leave your answer in terms of

A)
B)
C)
D)

Question 33

Solve the problem.
An angle above the horizontal is called an angle of elevation, and an angle below the horizontal is called an angle of depression. An airline passenger sees a lake at an angle of depression If the plane is flying at an altitude of 28,000 feet, find the
Distance from the plane to the lake to the nearest mile.

A) 90,610 miles
B) 17 miles
C) 51 miles
D) 16 miles

Question 34

Provide an appropriate response.
Find the exact value of cos

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

Question 35

Use a calculator to find the acute angle θ , to the nearest degree, that satisfies the equation.
tan θ = 1.7

A)
B)
C)
D)

Question 36

Provide an appropriate response.
Convert to radian measure. Leave your answer in terms of

A)
B)
C)
D)

Question 37

Provide an appropriate response.
Find the exact value of cos .

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

Question 38

Provide an appropriate response.
Evaluate cos 56π .

A)
B)
C)
D)

Question 39

Solve the problem.
An 8-foot-tall digital display showing airport arrivals and departures is mounted on a wall so that the bottom of the display is 12 feet above the floor. A woman whose eyes are 5 feet above the floor stands 42 feet away from
The wall. Find the angle (to the nearest degree) between the top and bottom of the display as seen by the
Woman.

A)
B)
C)
D)

Question 40

Provide an appropriate response.
Evaluate sin

A)
B)
C)
D)

Question 41

Find the derivative.
y =

A)
B)
C)
D)

Question 42

Find the derivative.

A)
B)
C)
D)

Question 43

Provide an appropriate response.
Use a calculator to find the value (to four decimal places) of sin

A) -0.8712
B) -0.6225
C) 0.8712
D) 0.6225

Question 44

Provide an appropriate response.
Use a calculator to find the value (to four decimal places) of sin

A) 0.5588
B) 0.8116
C) 0.5843
D) 1.3891

Question 45

Find the derivative.
y = 8x sin 17x

A) 136x cos 8x + 8 sin 17x
B) -136x cos 17x + 8 sin 17x
C) 136x cos 17x + 8 sin 17x
D) 136x cos 17x + sin 17x

Question 46

Find the derivative.

A)
B)
C)
D)

Question 47

Find the derivative.
y = 8 cos 8x

A) 8 sin 8x
B) 64 sin 8x
C) -64 sin 8x
D) -8 sin 8x

Question 48

Provide an appropriate response.
Use a calculator to find the value (to four decimal places) of cos

A) 0.3919
B) 0.6008
C) 0.7994
D) 0.9927

Question 49

Find the derivative.

A)
B)
C)
D)

Question 50

Find the derivative.
y =

A)
B)
C)
D)

Question 51

Use a graphing calculator to graph the function using the given viewing window parameters.

A)
B)
C)
D)

Question 52

Provide an appropriate response.
Use a calculator to find the function value to four decimal places. csc

A) 1.0105
B) 0.1450
C) 6.9688
D) 7.9688

Question 53

Find the derivative.

A)
B)
C)
D)

Question 54

Provide an appropriate response.
Use a calculator to find the value (to four decimal places) of sin

A) 0.4462
B) -0.9890
C) -0.9877
D) 0.3665

Question 55

Provide an appropriate response.
Use a calculator to find the function value to four decimal places. cot °

A) 0.8854
B) 0.5250
C) 0.5884
D) 1.9047

Question 56

Use a graphing calculator to graph the function using the given viewing window parameters.

A)
B)
C)
D)

Question 57

Find the derivative.

A)
B)
C)
D)

Question 58

Find the derivative.
y = 5 sin (4x - 8)

A)
B)
C)
D)

Question 59

Solve the problem.
The temperature in Fairbanks s approximated by temperature on day x, with x = 1 corresponding to Jan 1 and x = 365 corresponding to Dec 31. Estimate the temperature, to the nearest degree, on day 8.

A)
B)
C)
D)

Question 60

Solve the problem.
Sales of snow shovels are seasonal. Suppose the sale of snow shovels (in dollars) in Maine is approximated by s(t) = 10,000 + 10,000 cos t, where t is time in months and t = 0 is October. What are the sales in December?

A) $17,071
B) $18,660
C) $15,000
D) $13,900

Question 61

Provide an appropriate response.
Graph the function y = sin πx.

A)
B)
C)
D)

Question 62

Provide an appropriate response.
Find the indefinite integral

A)
B)
C)
D)

Question 63

Provide an appropriate response.
Graph the function

A)
B)
C)
D)

Question 64

Provide an appropriate response.
Find the indefinite integral

A)
B)
C)
D)

Question 65

Provide an appropriate response.
Find the indefinite integral

A)
B) - 2 cos t - 5 sin (5t) + C
C)
D)

Question 66

Provide an appropriate response.
The given graph is that of the derivative of a function f. Using information obtained from the graph of f' and the
fact that , sketch the graph of f.

Question 67

Provide an appropriate response.
Graph the function y = x cos x.

A)
B)
C)
D)

Question 68

Find the derivative.

A)
B)
C)
D)

Question 69

Solve the problem.
The revenue from the sale of electric blankets is seasonal, with maximum revenue in the winter. Let the revenue received from the sale of heaters be approximated by where x is time in years,
Measured from January 1. Find R'(x) fo r August 1st.

A)
B)
C)
D) 0

Question 70

Provide an appropriate response.
Find the indefinite integral

A)
B)
C)
D)

Question 71

Find the derivative.

A)
B)
C)
D)

Question 72

Provide an appropriate response.
Integrate:

A)
B)
C)
D)

Question 73

Provide an appropriate response.
Find the slope of the graph

A)
B)
C)
D)

Question 74

Provide an appropriate response.
Find the indefinite integral .

A) - 24 cos (6x) + C
B)
C)
D) 4 cos (6x) + C

Question 75

Provide an appropriate response.
Find the indefinite integral

A)
B)
C)
D)

Question 76

Solve the problem.
The intensity of light I at time t hours after sunrise and at a depth of x feet below the ocean surface is given by where D is the length of daylight in hours, Io is the intensity of light on the surface of the water at midday, and k is a positive constant. Assume In a study of the effect
Of light on ocean plants, a scientist needs to determine the minimum depth x at which a plant would never at
Any time be exposed to an intensity of light greater than 25. What is this minimum depth?

A) 385 ft
B) 108 ft
C) 139 ft
D) 65 ft

Question 77

Provide an appropriate response.
Use a graphing calculator to estimate ) for the given value of a.

A) 3.2871
B)
C) 1.4726
D) 1.9726

Question 78

Provide an appropriate response.
Find the slope of the graph

A)
B)
C)
D)

Question 79

Find the derivative.

A)
B)
C)
D)

Question 80

Solve the problem.
The profit for the sale of tennis rackets in a sporting goods store is given approximately by where P(t) is profit in thousands of dollars for a week of sales t weeks after January 1. What is the rate of change of profit six weeks after the first of the year? (Express the answer to the
Nearest dollar.)

A) $1793 per week
B) $8560 per week
C) $734 per week
D) $199 per week