Deck 27: Graphs of Sine and Cosine Functions

Question 1

Select the graph of the function.(Include two full periods. ) ​
Y = sin 2x
​

A)
B)
C)
D)
E)

Answer 1

Question 2

Select the graph of the function.(Include two full periods. )​ $$y = - \sin \frac { 8 \pi x } { 3 }$$ ​

A)
B)​
C)
D)
E)

Answer 2

Question 3

Find the period and amplitude. ​
Y = 7 sin 40x
​

A)Period: π;Amplitude: -7
B)Period: π;Amplitude: $\frac { 1 } { 7 }$
C)Period: $\frac { \pi } { 20 }$ ;Amplitude: $- \frac { 1 } { 7 }$
D)Period: 2π;Amplitude: 1
E)Period: $\frac { \pi } { 20 }$ ;Amplitude: 7

Answer 3

Period: $\frac { \pi } { 20 }$ ;Amplitude: 7

Question 4

Find the period and amplitude.​ $$y = \frac { 4 } { 5 } \cos \frac { 4 x } { 5 }$$ ​

A)Period: 2π;Amplitude: 1
B)Period: $\frac { \pi } { 2 }$ ;Amplitude: $\frac { 1 } { 5 }$
C)Period: π;Amplitude: $\frac { 5 } { 4 }$
D)Period: π;Amplitude: 5
E)Period: $\frac { 5 \pi } { 2 }$ ;Amplitude: $\frac { 4 } { 5 }$

Question 5

Write an equation for the function that is described by the given characteristics. ​
A cosine curve with a period of π,an amplitude of 6,a left phase shift of π,and a vertical translation down $\frac { 4 } { 3 }$ units.
​

A) $y = 6 \cos ( 2 x + \pi ) - \frac { 4 } { 3 }$
B) $y = 6 \cos ( 2 x + 2 \pi ) - \frac { 4 } { 3 }$
C) $y = 6 \cos ( 2 x + 2 \pi ) + \frac { 4 } { 3 }$
D) $y = 6 \cos ( x + 2 \pi ) - \frac { 4 } { 3 }$
E) $y = 6 \cos ( x + \pi ) - \frac { 4 } { 3 }$

Question 6

Find the period and amplitude.​ $$y = \frac { 4 } { 5 } \sin 2 \pi x$$ ​

A)Period: 1;Amplitude: $\frac { 4 } { 5 }$
B)Period: π;Amplitude: $\frac { 5 } { 4 }$
C)Period: 2π;Amplitude: 1
D)Period: $\frac { \pi } { 2 }$ ;Amplitude: $\frac { 1 } { 5 }$
E)Period: π;Amplitude: 5

Question 7

For a person at rest,the velocity v (in liters per second)of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next)is given by​ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ , ​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
​
Find the number of cycles per minute.
​

A)14 cycles/min
B)11 cycles/min
C)10 cycles/min
D)15 cycles/min
E)12 cycles/min

Question 8

Use a graphing utility to select the graph of the function.Include two full periods.​ $$y = \frac { 1 } { 100 } \sin 110 \pi t$$ ​

A)​
B)
C)
D)
E)

Question 9

Find the period and amplitude. ​
Y = -7 sin x
​

A)Period: π;Amplitude: -7
B)Period: π;Amplitude: $\frac { 1 } { 7 }$
C)Period: 2π;Amplitude: 7
D)Period: 2π;Amplitude: $- \frac { 1 } { 7 }$
E)Period: 2π;Amplitude: 1

Question 10

Select the graph of the function.(Include two full periods. )​ $$y = 4 + \frac { 1 } { 10 } \cos 60 \pi x$$ ​

A)
B)
C)
D)
E)

Question 11

Select the graph of the function.(Include two full periods. )​ $$y = 2 - \sin \frac { 2 \pi x } { 3 }$$ ​

A)
B)
C)
D)
E)

Question 12

For a person at rest,the velocity v (in liters per second)of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next)is given by​ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ , ​
Where t is the time (in seconds).
(Inhalation occurs when v > 0,and exhalation occurs when v < 0. )
​
Find the time for one full respiratory cycle.
​

A)7 sec
B)9 sec
C)3 sec
D)8 sec
E)6 sec

Question 13

For a person at rest,the velocity v (in liters per second)of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next)is given by​ $v = 0.85 \sin \left( \frac { \pi t } { 4 } \right)$ , ​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
Select the graph of this velocity function.
​

A)
B)
C)
D)
E)

Question 14

Use a graphing utility to select the graph of the function.Include two full periods. ​
Y = -2 sin (2x + π)
​

A)
B)
C)
D)
E)

Question 15

Use a graphing utility to select the graph of the function.Include two full periods. $$y = - 2 \sin \left( \frac { 8 } { 3 } x - \frac { \pi } { 3 } \right)$$ ​

A)
B)
C)​
D)
E)

Question 16

Select the graph of the function.(Include two full periods. )​ $$y = - 6 \cos \frac { \pi x } { 3 }$$ ​

A)
B)
C)
D)
E)

Question 17

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of π,an amplitude of 4,a right phase shift of $$\frac { \pi } { 2 }$$ ,and a vertical translation up 7 units.
​

A)y = 10 + 4 sin (2x + π)
B)y = 7 + 4 sin (2x - π)
C)​y = 9 - 4 sin (2x + π)
D)y = 8 + 4 sin (- 2x - π)
E)y = 11 + 7 sin (2x - π)

Question 18

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of 4π,an amplitude of 4,a left phase shift of $\frac { \pi } { 4 }$ ,and a vertical translation down 5 units.
​

A) $y = 4 \sin \left( x + \frac { \pi } { 8 } \right) - 5$
B) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 5$$
C) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 5$$
D) $y = 4 \sin \left( \frac { x } { 2 } + \pi \right) - 5$
E) $y = 5 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 4$

Question 19

Write an equation for the function that is described by the given characteristics. ​
A cosine curve with a period of 4π,an amplitude of 7,a right phase shift of $\frac { \pi } { 2 }$ ,and a vertical translation up 2 units.
​

A) $y = 2 + 7 \cos \left( \frac { x } { 2 } - \frac { \pi } { 4 } \right)$
B) $y = 2 + 7 \cos \left( \frac { x } { 2 } + \pi \right)$
C) $y = 2 - 7 \cos \left( \frac { x } { 2 } - \frac { \pi } { 4 } \right)$
D) $y = 2 + 7 \cos \left( \frac { x } { 2 } - \pi \right)$
E) $y = 2 + 7 \cos ( x - \pi )$

Question 20

Select the graph of the function.(Include two full periods. )​ $$y = \cos \frac { x } { 4 }$$ ​

A)
B)
C)
D)
E)

Question 21

The daily consumption C (in gallons)of diesel fuel on a farm is modeled by​ $C = 30.5 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.3 \right)$ , ​
Where t is the time (in days),with t = 1 corresponding to January 1.
Use a graphing utility to select the graph of the model.
​

A)
B)
C)
D)
E)

Question 22

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , ​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
​
Find the number of cycles per minute.
​

A)12 cycles/min
B)10 cycles/min
C)15 cycles/min
D)13 cycles/min
E)11 cycles/min

Question 23

The daily consumption C (in gallons)of diesel fuel on a farm is modeled by​ $C = 30.8 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.9 \right)$ , ​
Where t is the time (in days),with t = 1 corresponding to January 1.
What is the period of the model?
​

A)31 days
B)22 days
C)183 days
D)365 days
E)30 days

Question 24

Find a,b,and c for the function f(x)= a cos (bx - c)such that the graph of f(x)matches the graph below.

A)a = -2;b = -1;c= $- \frac { 3 } { 2 }$
B)a = 4;b = 1;c = π
C)a = 1;b = 2;c = -1
D)a = 2;b = 1;c = -π
E)a = 2;b = 1;c = $- \frac { 1 } { 2 }$ π

Question 25

Use a graphing utility to graph the function below.Be sure to include at least two full periods. $$y = - \sqrt { 2 } \sin \left( \frac { \pi x } { 2 } - \frac { \pi } { 4 } \right)$$

A)
B)
C)
D)
E)

Question 26

When tuning a piano,a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​
Y = 0.001 sin 850πt,
​
Where t is the time (in seconds).
​
The frequency is given by f = 1 / p.What is the frequency of the note?
​

A)85 cycles/sec
B) $$\frac { 1 } { 425 }$$ cycles/sec
C) $$\frac { 1 } { 850 }$$ cycles/sec
D)850 cycles/sec
E)425 cycles/sec

Question 27

Determine which of the graphs below represents the following function y=|x|sin x
​

A)
B)
C)
D)
E)

Question 28

​Sketch the graph of the function below,being sure to include at least two full periods. ​
​y = 2 cos​( x - $\frac { \pi } { 2 }$ )​ ​

A)​
B)​
C)​
D)​
E)​

Question 29

When tuning a piano,a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​
Y = 0.001 sin 880πt,
​
Where t is the time (in seconds).
​
What is the period of the function?
​

A) $\frac { 1 } { 880 }$ sec
B)440 sec
C) $\frac { 1 } { 440 }$ sec
D)880 sec
E)88 sec

Question 30

The daily consumption C (in gallons)of diesel fuel on a farm is modeled by​ $C = 30.4 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.2 \right)$ , ​
Where t is the time (in days),with t = 1 corresponding to January 1.
What is the average daily fuel consumption?
​

A)365 gal.
B)21.6 gal.
C)30 gal.
D)10.2 gal.
E)30.4 gal.

Question 31

Sketch the graph of the function below,being sure to include at least two full periods. ​
Y = - cos(x+ $\frac { \pi } { 2 }$ ) ​

A)​
B)​
C)​
D)​
E)​

Question 32

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , ​
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
Select the graph of this velocity function.

A)
B)
C)
D)
E)​

Question 33

​Determine the period and amplitude of the following function​ $$y = 3 \cos \left( \frac { 2 x } { 3 } - \frac { 1 } { 6 } \right)$$ ​

A)​Period: 10 $\pi$ ;Amplitude: 6
B)​Period: $\frac { \pi } { 5 }$ ;Amplitude: 3
C)​Period: 8 $\pi$ ;Amplitude: 4
D)​Period: $\pi$ ;Amplitude: 3
E)​Period: 5 $\pi$ ;Amplitude: 2

Question 34

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
​
Find the time for one full respiratory cycle.​
​

A)6 sec
B)2 sec
C)7 sec
D)3 sec
E)8 sec

Question 35

​Determine the period and amplitude of the following function​ $$y = 5 \cos \left( \frac { 5 x } { 7 } + \frac { 1 } { 3 } \right)$$ ​

A)​Period: 16 $\pi$ ;Amplitude: 10
B)​Period: $\pi$ ;Amplitude: 5
C)​Period: 5 $\pi$ ;Amplitude: 6
D)​Period: $\frac { \pi } { 2 }$ ;Amplitude: 5
E)​Period: 8 $\pi$ ;Amplitude: 4

Question 36

Find a and d for the function f(x)= a sin x + d such that the graph of f(x)matches the graph below.

A)a = 2;d = -1
B)a = 4;d = 1
C)a = -2;d = 1
D)a = 2;d = 2
E)a = 4;d = -3

Question 37

Use a graphing utility to graph the function below.Be sure to include at least two full periods. y = 4 sin (x - 5π)+ 1

A)
B) ​
C) ​
D) ​
E) ​