Question 1

Find the phase shift of the function.
-$$y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  2 units down 
B)  2 units up 
C)  $\frac { \pi } { 2 }$ units to the left 
D)  $\frac { \pi } { 2 }$ units to the right 
A)  2 units down 
B)  2 units up 
C)  $\frac { \pi } { 2 }$ units to the left 
D)  $\frac { \pi } { 2 }$ units to the right

Question 2

Determine the equation of the graph.
-A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Accepted Answer

A)  $\mathrm { s } ( \mathrm { t } ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 10 } } \mathrm { t }$ 
B)  $s ( t ) = 2 \sin \sqrt { \frac { 1 } { 5 } } t$ 
C)  $s ( t ) = 2 \sin \sqrt { 5 } t$ 
D)  $s ( t ) = 5 \sin \sqrt { 2 } t$ 
A)  $\mathrm { s } ( \mathrm { t } ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 10 } } \mathrm { t }$ 
B)  $s ( t ) = 2 \sin \sqrt { \frac { 1 } { 5 } } t$ 
C)  $s ( t ) = 2 \sin \sqrt { 5 } t$ 
D)  $s ( t ) = 5 \sin \sqrt { 2 } t$

Question 3

Give the amplitude or period as requested.
-Amplitude of $y = - 4 \sin x$

Accepted Answer

A)  $2 \pi$ 
B)  $- 4 \pi$ 
C)  4 
D)  $\frac { \pi } { 4 }$ 
A)  $2 \pi$ 
B)  $- 4 \pi$ 
C)  4 
D)  $\frac { \pi } { 4 }$

Question 4

Convert the degree measure to radians, correct to four decimal places. $$3.1416 \text { for } \pi \text {. }$$
-$29.4905 ^ { \circ }$

Accepted Answer

A)  $0.4147$ 
B)  $0.5147$ 
C)  $0.7147$ 
D)  $0.6147$ 
A)  $0.4147$ 
B)  $0.5147$ 
C)  $0.7147$ 
D)  $0.6147$

Question 5

Find the phase shift of the function.
-$$y = 4 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  $\pi$ units to the right 
B)  $\pi$ units to the left 
C)  $\frac { \pi } { 16 }$ units to the left 
D)  $\frac { \pi } { 4 }$ units to the right 
A)  $\pi$ units to the right 
B)  $\pi$ units to the left 
C)  $\frac { \pi } { 16 }$ units to the left 
D)  $\frac { \pi } { 4 }$ units to the right

Question 6

Determine the equation of the graph.
-A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ sec, what is the frequency of the system?

Accepted Answer

A)  $\frac { 2 \pi } { 3 }$ cycles per sec 
B)  $\frac { 2 } { 3 \pi }$ cycles per sec 
C)  3 cycles per sec 
D)  6 cycles per sec 
A)  $\frac { 2 \pi } { 3 }$ cycles per sec 
B)  $\frac { 2 } { 3 \pi }$ cycles per sec 
C)  3 cycles per sec 
D)  6 cycles per sec

Question 7

Solve the problem
-A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 15 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Accepted Answer

A)  3 radians per sec 
B)  $\frac { 1 } { 3 }$ radians per sec 
C)  75 radians per sec 
D)  $\frac { 1 } { 75 }$ radian per sec 
A)  3 radians per sec 
B)  $\frac { 1 } { 3 }$ radians per sec 
C)  75 radians per sec 
D)  $\frac { 1 } { 75 }$ radian per sec

Question 8

Graph the function.
-$y=-2-\tan \left(x+\frac{\pi}{4}\right)$

Accepted Answer

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

Question 9

Determine the equation of the graph.
-A weight attached to a spring is pulled down 8 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Accepted Answer

A)  $s ( t ) = 8 \cos 10 t$ 
B)  $s ( t ) = - 8 \cos 5 t$ 
C)  $s ( t ) = 8 \cos 5 t$ 
D)  $s ( t ) = - 8 \cos 10 t$ 
A)  $s ( t ) = 8 \cos 10 t$ 
B)  $s ( t ) = - 8 \cos 5 t$ 
C)  $s ( t ) = 8 \cos 5 t$ 
D)  $s ( t ) = - 8 \cos 10 t$

Question 10

Graph the function.
-$$y = \sin \frac { 3 } { 2 } x$$

Accepted Answer

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

Question 11

Convert the degree measure to radians, correct to four decimal places. $$3.1416 \text { for } \pi \text {. }$$
-$16 ^ { \circ } 30 ^ { \prime }$

Accepted Answer

A)  $0.2880$ 
B)  $0.4880$ 
C)  $0.1880$ 
D)  $0.5880$ 
A)  $0.2880$ 
B)  $0.4880$ 
C)  $0.1880$ 
D)  $0.5880$

Question 12

Graph the function.
-$$y = \sin \pi x$$

Accepted Answer

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

Question 13

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-

Accepted Answer

A)  $y = - 3 \sin ( 2 x )$ 
B)  $y = 3 \sin ( 2 x )$ 
C)  $y = 3 \cos \left( \frac { 1 } { 2 } x \right)$ 
D)  $y = - 3 \cos ( 2 x )$ 
A)  $y = - 3 \sin ( 2 x )$ 
B)  $y = 3 \sin ( 2 x )$ 
C)  $y = 3 \cos \left( \frac { 1 } { 2 } x \right)$ 
D)  $y = - 3 \cos ( 2 x )$

Question 14

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A car wheel has a 14 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward $3 \mathrm { ft }$ ?

Accepted Answer

A)  $147.3 ^ { \circ }$ 
B)  $157.3 ^ { \circ }$ 
C)  $162.3 ^ { \circ }$ 
D)  $152.3 ^ { \circ }$ 
A)  $147.3 ^ { \circ }$ 
B)  $157.3 ^ { \circ }$ 
C)  $162.3 ^ { \circ }$ 
D)  $152.3 ^ { \circ }$

Question 15

Find the exact value of s in the given interval that has the given circular function value.
-$\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

Accepted Answer

A)  $s = \frac { 5 \pi } { 4 }$ 
B)  $s = \frac { 4 \pi } { 3 }$ 
C)  $\mathrm { s } = \frac { \pi } { 3 }$ 
D)  $s = \frac { 7 \pi } { 6 }$ 
A)  $s = \frac { 5 \pi } { 4 }$ 
B)  $s = \frac { 4 \pi } { 3 }$ 
C)  $\mathrm { s } = \frac { \pi } { 3 }$ 
D)  $s = \frac { 7 \pi } { 6 }$

Question 16

The function graphed is of the form y $$y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$$ etermine the equation of the graph.
-

Accepted Answer

A)  $y = 2 \tan x$ 
B)  $y = 2 \cot x$ 
C)  $y = \cot 2 x$ 
D)  $y = \tan 2 x$ 
A)  $y = 2 \tan x$ 
B)  $y = 2 \cot x$ 
C)  $y = \cot 2 x$ 
D)  $y = \tan 2 x$

Question 17

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 10 minutes. Give an exact answer.

Accepted Answer

A)  $1.5 \pi$ in. 
B)  $9 \pi$ in. 
C)  $6 \pi$ in. 
D)  $3 \pi$ in. 
A)  $1.5 \pi$ in. 
B)  $9 \pi$ in. 
C)  $6 \pi$ in. 
D)  $3 \pi$ in.

Question 18

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$
-$810 ^ { \circ }$

Accepted Answer

A)  $- \frac { 9 \pi } { 2 }$ 
B)  $- \frac { 9 \pi } { 4 }$ 
C)  $\frac { 9 \pi } { 2 }$ 
D)  $9 \pi$ 
A)  $- \frac { 9 \pi } { 2 }$ 
B)  $- \frac { 9 \pi } { 4 }$ 
C)  $\frac { 9 \pi } { 2 }$ 
D)  $9 \pi$

Question 19

Find the corresponding angle measure in radians.
-$-45^{\circ}$

Accepted Answer

A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$ 
A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { \pi } { 3 }$

Question 20

The function graphed is of the form y $$y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$$ etermine the equation of the graph.
-

Accepted Answer

A)  $y = - 2 \cot 2 x$ 
B)  $y = - 2 \tan 2 x$ 
C)  $y = 2 \cot 2 x$ 
D)  $y = - 2 \cot x$ 
A)  $y = - 2 \cot 2 x$ 
B)  $y = - 2 \tan 2 x$ 
C)  $y = 2 \cot 2 x$ 
D)  $y = - 2 \cot x$

Find the phase shift of the function. - $y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)$

Determine the equation of the graph. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Give the amplitude or period as requested. -Amplitude of $y = - 4 \sin x$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $29.4905 ^ { \circ }$

Find the phase shift of the function. - $y = 4 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 4 } \right)$

Determine the equation of the graph. -A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ sec, what is the frequency of the system?

Solve the problem -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 15 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Graph the function. - $y=-2-\tan \left(x+\frac{\pi}{4}\right)$ $Graph the function. - y=-2-\tan \left(x+\frac{\pi}{4}\right)$

Determine the equation of the graph. -A weight attached to a spring is pulled down 8 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Graph the function. - $y = \sin \frac { 3 } { 2 } x$ $Graph the function. - y = \sin \frac { 3 } { 2 } x$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $16 ^ { \circ } 30 ^ { \prime }$

Graph the function. - $y = \sin \pi x$ $Graph the function. - y = \sin \pi x$

The function graphed is of the form y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$ Determine the equation of the graph. - $The function graphed is of the form y y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0 Determine the equation of the graph. -$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A car wheel has a 14 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward $3 \mathrm { ft }$ ?

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 10 minutes. Give an exact answer.

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $810 ^ { \circ }$

Find the corresponding angle measure in radians. - $-45^{\circ}$ $Find the corresponding angle measure in radians. - -45^{\circ}$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 7: The Circular Functions and Their Graphs

Find the phase shift of the function. - y=−2sin⁡(x−π2)y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)y=−2sin(x−2π​)

Determine the equation of the graph. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched 2ft2 \mathrm { ft }2ft and released. What is the equation for the resulting oscillatory motion?

Give the amplitude or period as requested. -Amplitude of y=−4sin⁡xy = - 4 \sin xy=−4sinx

Convert the degree measure to radians, correct to four decimal places. 3.1416 for π. 3.1416 \text { for } \pi \text {. }3.1416 for π. - 29.4905∘29.4905 ^ { \circ }29.4905∘

Find the phase shift of the function. - y=4sin⁡(14x−π4)y = 4 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 4 } \right)y=4sin(41​x−4π​)

Determine the equation of the graph. -A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming that the period of the system is 13\frac { 1 } { 3 }31​ sec, what is the frequency of the system?

Solve the problem -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 15 seconds a central angle of 15\frac { 1 } { 5 }51​ radian has been covered, what is the angular speed of the ball?

Graph the function. - y=−2−tan⁡(x+π4)y=-2-\tan \left(x+\frac{\pi}{4}\right)y=−2−tan(x+4π​)

Graph the function. - y=sin⁡32xy = \sin \frac { 3 } { 2 } xy=sin23​x

Convert the degree measure to radians, correct to four decimal places. 3.1416 for π. 3.1416 \text { for } \pi \text {. }3.1416 for π. - 16∘30′16 ^ { \circ } 30 ^ { \prime }16∘30′

Graph the function. - y=sin⁡πxy = \sin \pi xy=sinπx

The function graphed is of the form y y=asin⁡bx or y=acos⁡bx, where b>0y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0y=asinbx or y=acosbx, where b>0 Determine the equation of the graph. -

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A car wheel has a 14 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 3ft3 \mathrm { ft }3ft ?

Find the exact value of s in the given interval that has the given circular function value. - [π,3π2];sin⁡s=−32\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }[π,23π​];sins=−23​​

The function graphed is of the form y y=atan⁡bx or y=acot⁡bx, where b>0. y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }y=atanbx or y=acotbx, where b>0. etermine the equation of the graph. -

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 10 minutes. Give an exact answer.

Convert the degree measure to radians. Leave answer as a multiple of π.\pi .π. - 810∘810 ^ { \circ }810∘

Find the corresponding angle measure in radians. - −45∘-45^{\circ}−45∘

The function graphed is of the form y y=atan⁡bx or y=acot⁡bx, where b>0. y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }y=atanbx or y=acotbx, where b>0. etermine the equation of the graph. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Find the phase shift of the function. - $y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)$

Determine the equation of the graph. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Give the amplitude or period as requested. -Amplitude of $y = - 4 \sin x$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $29.4905 ^ { \circ }$

Find the phase shift of the function. - $y = 4 \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 4 } \right)$

Determine the equation of the graph. -A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 3 }$ sec, what is the frequency of the system?

Solve the problem -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 15 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Graph the function. - $y=-2-\tan \left(x+\frac{\pi}{4}\right)$ $Graph the function. - y=-2-\tan \left(x+\frac{\pi}{4}\right)$

Graph the function. - $y = \sin \frac { 3 } { 2 } x$ $Graph the function. - y = \sin \frac { 3 } { 2 } x$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $16 ^ { \circ } 30 ^ { \prime }$

Graph the function. - $y = \sin \pi x$ $Graph the function. - y = \sin \pi x$

The function graphed is of the form y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$ Determine the equation of the graph. - $The function graphed is of the form y y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0 Determine the equation of the graph. -$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A car wheel has a 14 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward $3 \mathrm { ft }$ ?

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $810 ^ { \circ }$

Find the corresponding angle measure in radians. - $-45^{\circ}$ $Find the corresponding angle measure in radians. - -45^{\circ}$