Question 1

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

Accepted Answer

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 
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 2

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

Accepted Answer

A)    
B)    ​ 
C)    ​ 
D)    ​ 
E)    ​ 
A)    
B)    ​ 
C)    ​ 
D)    ​ 
E)    ​

Question 3

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

Accepted Answer

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 
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

Question 4

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.
​

Accepted Answer

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)  $y = 6 \cos ( x + \pi ) - \frac { 4 } { 3 }$ 
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 5

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

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.
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

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

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 8

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.

Accepted Answer

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 
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 9

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

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.
​

Accepted Answer

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

Question 11

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

Accepted Answer

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: $\frac { 4 } { 5 }$ 
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 12

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

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?
​

Accepted Answer

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

Question 14

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

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.​
​

Accepted Answer

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

Question 16

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?
​

Accepted Answer

A) 85 cycles/sec 
B)  $$\frac { 1 } { 425 }$$ cycles/sec 
C)  $$\frac { 1 } { 850 }$$ cycles/sec 
D) 850 cycles/sec 
E) 425 cycles/sec 
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 17

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.
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Exam 27: Graphs of Sine and Cosine Functions

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

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

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

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 43\frac { 4 } { 3 }34​ units. ​

Use a graphing utility to graph the function below.Be sure to include at least two full periods. y=−2sin⁡(πx2−π4)y = - \sqrt { 2 } \sin \left( \frac { \pi x } { 2 } - \frac { \pi } { 4 } \right)y=−2​sin(2πx​−4π​)

​Sketch the graph of the function below,being sure to include at least two full periods. ​ ​y = 2 cos​( x - π2\frac { \pi } { 2 }2π​ )​ ​

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.

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

Find the period and amplitude.​ y=45cos⁡4x5y = \frac { 4 } { 5 } \cos \frac { 4 x } { 5 }y=54​cos54x​ ​

Select the graph of the function.(Include two full periods. )​ y=−6cos⁡πx3y = - 6 \cos \frac { \pi x } { 3 }y=−6cos3πx​ ​

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? ​

Select the graph of the function.(Include two full periods. )​ y=cos⁡x4y = \cos \frac { x } { 4 }y=cos4x​ ​

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? ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

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Nonlinear Inequalities

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Properties of Logarithms

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Trigonometric Functions The Unit Circle

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Using Fundamental Identities

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Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

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Trigonometric Form of a Complex Number

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Linear Programming

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Mathematical Induction

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Lines

Introduction to Conics Parabolas

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Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

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

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.

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

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

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

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

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

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?

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

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?