Deck 4: Graphs of the Circular Functions

Question 1

Determine the equation of the graph.
Determine the equation of the graph.

Answer 1

A

Question 2

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Answer 2

D

Question 3

Graph the function.
8

Answer 3

C

Question 4

Match the function with its graph.

Question 5

Graph the function.
7

Question 6

Find the phase shift of the function.

Question 7

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Question 8

Use Identities to find the exact value.
A rotating beacon is located 15 ft from a wall. The distance from the beacon to the point on the wall where the beacon is aimed is given by

Question 9

Find the phase shift of the function.

Question 10

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Question 11

Match the function with its graph.
13)y )y == si3 n si3n xx 2)4)y y == cos 3 cos x3x

Question 12

Graph the function.

Question 13

Find the phase shift of the function.

Question 14

Graph the function.

Question 15

Graph the function.
12

Question 16

Graph the function over a one-period interval.
11

Question 17

Use Identities to find the exact value.

Question 18

Graph the function.

Question 19

Use Identities to find the exact value.
Tides go up and down in a 14.8-hour period. The average depth of a certain river is 7 m and ranges from 4 to 10 m. The variation can be approximated by a sine curve. Write an equation that gives the
Approximate variation y, if x is the number of hours after midnight and high tide occurs at 5:00 am.

Question 20

Give the amplitude or period as requested.

Question 21

Graph the function.

Question 22

Graph the function.

Question 23

Find the phase shift of the function.

Question 24

Find the phase shift of the function.

Question 25

Solve the problem.

Question 26

Find the specified quantity.

Question 27

Solve the problem.
Determine the period and frequency of oscillation when a pendulum of length 9 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Question 28

Match the function with its graph.

Question 29

Graph the function.

Question 30

Graph the function.

Question 31

Graph the function.
25

Question 32

Match the function with its graph.

Question 33

Give the amplitude or period as requested.
Period of y = sin 3x

Question 34

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Question 35

Graph the function.

Question 36

Solve the problem.
A guitar string is plucked so that it vibrates with a frequency of F = 66. Suppose the maximum displacement at the center of the string is s(0)= 0.58. Find an equation of the form s(t)= a cos bt to
Model this displacement. Round constants to 2 decimal places.

A)s(t)= 0.58 cos 414.69t
B)s(t)= 0.58 cos 10.50t
C)s(t)= 1.16 cos 414.69t
D)s(t)= 1.16 cos 10.50t

Question 37

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph.

Question 38

Solve the problem.
The voltage E in an electrical circuit is given by E = 5.7 cos 110πt, where t is time measured in seconds. Find the amplitude.

A)11.4
B)5.7
C)110π
D)110

Question 39

Graph the function over a one-period interval.

Question 40

Give the amplitude or period as requested.

Question 41

Find the phase shift of the function.

Question 42

Graph the function.

Question 43

Find the phase shift of the function.

Question 44

Find the phase shift of the function.

Question 45

Solve the problem.
The chart represents the amount of fuel consumed by a machine used in manufacturing. The machine is turned on at the beginning of the day, takes a certain amount of time to reach its full
Power (the point at which it uses the most fuel per hour), runs for a certain number of hours, and is
Shut off at the end of the work day. The fuel usage per hour of the machine is represented by a
Periodic function. What is the period in hours of this function?

Question 46

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph.

Question 47

Give the amplitude or period as requested.

Question 48

Solve the problem.

Question 49

Match the function with its graph.
29

Question 50

Solve the problem.

Question 51

Determine the equation of the graph.

Question 52

Find the phase shift of the function.

Question 53

Graph the function.
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Question 54

Graph the function over a one-period interval.

Question 55

Find the phase shift of the function.

Question 56

Find the specified quantity.

Question 57

Find the specified quantity.

Question 58

Solve the problem.

Question 59

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Question 60

Graph the function.

Question 61

Solve the problem.

Question 62

Solve the problem.

Question 63

Graph the function.
50

Question 64

Graph the function over a one-period interval.

Question 65

Give the amplitude or period as requested.

Question 66

Graph the function.
36

Question 67

Solve the problem.

Question 68

Graph the function.

Question 69

Graph the function.
43

Question 70

Solve the problem.

Question 71

Graph the function.

Question 72

Graph the function.
42

Question 73

Graph the function.
49

Question 74

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph.

Question 75

Graph the function.

Question 76

Graph the function.

Question 77

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.

Question 78

Graph the function.
44

Question 79

Determine the equation of the graph.

Question 80

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph.