Question 1

Graph the function.
-$y=2 \sin \left(x-\frac{\pi}{3}\right)$

Accepted Answer

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

Question 2

Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }$ inches after $\mathrm { t }$ seconds. What are the frequency and period of the system?

Accepted Answer

A)  Frequency $= \frac { \pi } { 7 }$ cycles per sec, period $= \frac { 7 } { \pi } \mathrm { sec }$ 
B)  Frequency $= \frac { 7 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 7 } \mathrm { sec }$ 
C)  Frequency $= \frac { 7 } { \pi }$ cycles per sec, period $= \frac { \pi } { 7 } \mathrm { sec }$ 
D)  Frequency $= 7$ cycles per sec, period $= \frac { 1 } { 7 } \mathrm { sec }$ 
A)  Frequency $= \frac { \pi } { 7 }$ cycles per sec, period $= \frac { 7 } { \pi } \mathrm { sec }$ 
B)  Frequency $= \frac { 7 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 7 } \mathrm { sec }$ 
C)  Frequency $= \frac { 7 } { \pi }$ cycles per sec, period $= \frac { \pi } { 7 } \mathrm { sec }$ 
D)  Frequency $= 7$ cycles per sec, period $= \frac { 1 } { 7 } \mathrm { sec }$

Question 3

Describe how an angle measure can be converted from radians to degrees.

Accepted Answer

A)  Multiply the degree measure by $\frac { 180 ^ { \circ } } { \pi }$. 
B)  Multiply the degree measure by $\frac { 360 ^ { \circ } } { \pi }$. 
C)  Multiply the degree measure by $\frac { \pi } { 180 ^ { \circ } }$. 
D)  Multiply the degree measure by $\frac { \pi } { 90 ^ { \circ } }$. 
A)  Multiply the degree measure by $\frac { 180 ^ { \circ } } { \pi }$. 
B)  Multiply the degree measure by $\frac { 360 ^ { \circ } } { \pi }$. 
C)  Multiply the degree measure by $\frac { \pi } { 180 ^ { \circ } }$. 
D)  Multiply the degree measure by $\frac { \pi } { 90 ^ { \circ } }$.

Question 4

Find the exact circular function value.
-$$\sin \frac { - 5 \pi } { 4 }$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$

Question 5

Give the amplitude or period as requested.
-Period of $y = - 5 \cos x$

Accepted Answer

A)  $\frac { \pi } { 5 }$ 
B)  $2 \pi$ 
C)  5 
D)  $\pi$ 
A)  $\frac { \pi } { 5 }$ 
B)  $2 \pi$ 
C)  5 
D)  $\pi$

Question 6

Match the function with its graph.
-1) $y = \sin \frac { 1 } { 3 } x$
2) $y = \frac { 1 } { 3 } \cos x$
3) $y = \frac { 1 } { 3 } \sin x$
4) $y = \cos \frac { 1 } { 3 } x$

Accepted Answer

A)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$ 
B)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$ 
C)  $1 \mathrm {~A} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~B}$ 
D)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$ 
A)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$ 
B)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$ 
C)  $1 \mathrm {~A} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~B}$ 
D)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$

Question 7

Find the exact values of s in the given interval that satisfy the given condition.
-$$[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $\frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $\frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$ 
C)  $\frac { \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D)  $\frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
A)  $\frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $\frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$ 
C)  $\frac { \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D)  $\frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$

Question 8

Graph the function.
-$$y = \frac { 4 } { 3 } \cot x$$

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 3 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 7 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Accepted Answer

A)  $s ( t ) = 3 \pi \cos 7 t$ 
B)  $s ( t ) = - 3 \cos \frac { 7 } { \pi } t$ 
C)  $s ( t ) = 3 \cos 14 t$ 
D)  $s ( t ) = - 3 \cos 14 t$ 
A)  $s ( t ) = 3 \pi \cos 7 t$ 
B)  $s ( t ) = - 3 \cos \frac { 7 } { \pi } t$ 
C)  $s ( t ) = 3 \cos 14 t$ 
D)  $s ( t ) = - 3 \cos 14 t$

Question 10

Find the phase shift of the function.
-$$y = 5 \sin \left( 4 x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\frac { \pi } { 8 }$ units to the right 
C)  $4 \pi$ units down 
D)  $5 \pi$ units up 
A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\frac { \pi } { 8 }$ units to the right 
C)  $4 \pi$ units down 
D)  $5 \pi$ units up

Question 11

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 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Accepted Answer

A)  $36 \pi$ in. 
B)  $6 \pi$ in. 
C)  $12 \pi$ in. 
D)  $3 \pi \mathrm { in }$. 
A)  $36 \pi$ in. 
B)  $6 \pi$ in. 
C)  $12 \pi$ in. 
D)  $3 \pi \mathrm { in }$.

Question 12

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 total sales in dollars of some small businesses fluctuates according to the equation $\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \pi \mathrm { x } / 6$, where $\mathrm { x }$ is the time in months, with $\mathrm { x } = 1$ corresponding to January, $\mathrm { A } = 7700$, and $B = 3000$. Determine the month with the greatest total sales and give the sales in that month.

Accepted Answer

A)  December; $\$ 10,700$ 
B)  June; $\$ 7700$ 
C)  September; $\$ 4700$ 
D)  March; $\$ 10,700$ 
A)  December; $\$ 10,700$ 
B)  June; $\$ 7700$ 
C)  September; $\$ 4700$ 
D)  March; $\$ 10,700$

Question 13

Graph the function over a one-period interval.
-$y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

Accepted Answer

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

Question 14

Solve the problem
-Each tire of an automobile has a radius of $2.5$ feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 115 feet per sec? Round your answer to the nearest tenth.

Accepted Answer

A)  $439.3 \mathrm { rpm }$ 
B)  $2745.4 \mathrm { rpm }$ 
C)  $7.3 \mathrm { rpm }$ 
D)  $878.5 \mathrm { rpm }$ 
A)  $439.3 \mathrm { rpm }$ 
B)  $2745.4 \mathrm { rpm }$ 
C)  $7.3 \mathrm { rpm }$ 
D)  $878.5 \mathrm { rpm }$

Question 15

Determine the equation of the graph.
-The formula for the up and down motion of a weight on a spring is given by $s ( t ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$. If the spring constant is 5 , then what mass $\mathrm { m }$ must be used in order to produce a period of 6 seconds?

Accepted Answer

A)  $\frac { 4 } { \pi ^ { 2 } }$ 
B)  $\frac { 45 } { \pi ^ { 2 } }$ 
C)  $\frac { 5 \pi } { 2 }$ 
D)  $\frac { 2 \pi } { 5 }$ 
A)  $\frac { 4 } { \pi ^ { 2 } }$ 
B)  $\frac { 45 } { \pi ^ { 2 } }$ 
C)  $\frac { 5 \pi } { 2 }$ 
D)  $\frac { 2 \pi } { 5 }$

Question 16

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$
-$- 45 ^ { \circ }$

Accepted Answer

A)  $- \frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $- \frac { \pi } { 5 }$ 
A)  $- \frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 6 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $- \frac { \pi } { 5 }$

Question 17

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, $30 ^ { \circ } \mathrm { N }$, are $2234 \mathrm {~km}$ apart.

Accepted Answer

A)  $60 ^ { \circ } \mathrm { N }$ 
B)  $50 ^ { \circ } \mathrm { N }$ 
C)  $20 ^ { \circ } \mathrm { N }$ 
D)  $70 ^ { \circ } \mathrm { N }$ 
A)  $60 ^ { \circ } \mathrm { N }$ 
B)  $50 ^ { \circ } \mathrm { N }$ 
C)  $20 ^ { \circ } \mathrm { N }$ 
D)  $70 ^ { \circ } \mathrm { N }$

Question 18

Find the exact circular function value.
-$\cos 2 \pi$

Accepted Answer

A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  $- 1$ 
D)  0 
A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  $- 1$ 
D)  0

Question 19

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 voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.3 \cos 180 \pi \mathrm { t }$, where $\mathrm { t }$ is time measured in seconds. Find the amplitude.

Accepted Answer

A)  180 
B)  $180 \pi$ 
C)  $3.3$ 
D)  $6.6$ 
A)  180 
B)  $180 \pi$ 
C)  $3.3$ 
D)  $6.6$

Question 20

The function graphed is of the form $$y = \cos x + c , y = \sin x + c , y = \cos ( x - d ) , \text { or } y = \sin ( x - d )$$ where d is the least possible
positive value. Determine the equation of the graph.
-

Accepted Answer

A)  $y = \sin x - 4$ 
B)  $y = \sin x + 4$ 
C)  $y = \cos x - 4$ 
D)  $y = \cos ( x - 4 )$ 
A)  $y = \sin x - 4$ 
B)  $y = \sin x + 4$ 
C)  $y = \cos x - 4$ 
D)  $y = \cos ( x - 4 )$

Graph the function. - $y=2 \sin \left(x-\frac{\pi}{3}\right)$ $Graph the function. - y=2 \sin \left(x-\frac{\pi}{3}\right)$

Determine the equation of the graph. -The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }$ inches after $\mathrm { t }$ seconds. What are the frequency and period of the system?

Describe how an angle measure can be converted from radians to degrees.

Find the exact circular function value. - $\sin \frac { - 5 \pi } { 4 }$

Give the amplitude or period as requested. -Period of $y = - 5 \cos x$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y = \frac { 4 } { 3 } \cot x$ $Graph the function. - y = \frac { 4 } { 3 } \cot x$

Determine the equation of the graph. -A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 7 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Find the phase shift of the function. - $y = 5 \sin \left( 4 x - \frac { \pi } { 2 } \right)$

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 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Graph the function over a one-period interval. - $y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

Solve the problem -Each tire of an automobile has a radius of $2.5$ feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 115 feet per sec? Round your answer to the nearest tenth.

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $- 45 ^ { \circ }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, $30 ^ { \circ } \mathrm { N }$ , are $2234 \mathrm {~km}$ apart.

Find the exact circular function value. - $\cos 2 \pi$

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

Graph the function. - y=2sin⁡(x−π3)y=2 \sin \left(x-\frac{\pi}{3}\right)y=2sin(x−3π​)

Determine the equation of the graph. -The position of a weight attached to a spring is s(t)=−2cos⁡7t\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }s(t)=−2cos7t inches after t\mathrm { t }t seconds. What are the frequency and period of the system?

Describe how an angle measure can be converted from radians to degrees.

Find the exact circular function value. - sin⁡−5π4\sin \frac { - 5 \pi } { 4 }sin4−5π​

Give the amplitude or period as requested. -Period of y=−5cos⁡xy = - 5 \cos xy=−5cosx

Match the function with its graph. -1) y=sin⁡13xy = \sin \frac { 1 } { 3 } xy=sin31​x 2) y=13cos⁡xy = \frac { 1 } { 3 } \cos xy=31​cosx 3) y=13sin⁡xy = \frac { 1 } { 3 } \sin xy=31​sinx 4) y=cos⁡13xy = \cos \frac { 1 } { 3 } xy=cos31​x

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);cos⁡s=−32[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 3 } } { 2 }[0,2π);coss=−23​​

Graph the function. - y=43cot⁡xy = \frac { 4 } { 3 } \cot xy=34​cotx

Find the phase shift of the function. - y=5sin⁡(4x−π2)y = 5 \sin \left( 4 x - \frac { \pi } { 2 } \right)y=5sin(4x−2π​)

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 6 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Graph the function over a one-period interval. - y=12cos⁡4(x−π3)y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)y=21​cos4(x−3π​)

Solve the problem -Each tire of an automobile has a radius of 2.52.52.5 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 115 feet per sec? Round your answer to the nearest tenth.

Convert the degree measure to radians. Leave answer as a multiple of π.\pi .π. - −45∘- 45 ^ { \circ }−45∘

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30∘N30 ^ { \circ } \mathrm { N }30∘N , are 2234 km2234 \mathrm {~km}2234 km apart.

Find the exact circular function value. - cos⁡2π\cos 2 \picos2π

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

Graph the function. - $y=2 \sin \left(x-\frac{\pi}{3}\right)$ $Graph the function. - y=2 \sin \left(x-\frac{\pi}{3}\right)$

Determine the equation of the graph. -The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }$ inches after $\mathrm { t }$ seconds. What are the frequency and period of the system?

Find the exact circular function value. - $\sin \frac { - 5 \pi } { 4 }$

Give the amplitude or period as requested. -Period of $y = - 5 \cos x$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y = \frac { 4 } { 3 } \cot x$ $Graph the function. - y = \frac { 4 } { 3 } \cot x$

Find the phase shift of the function. - $y = 5 \sin \left( 4 x - \frac { \pi } { 2 } \right)$

Graph the function over a one-period interval. - $y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$ $Graph the function over a one-period interval. - y=\frac{1}{2} \cos 4\left(x-\frac{\pi}{3}\right)$

Solve the problem -Each tire of an automobile has a radius of $2.5$ feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 115 feet per sec? Round your answer to the nearest tenth.

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $- 45 ^ { \circ }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, $30 ^ { \circ } \mathrm { N }$ , are $2234 \mathrm {~km}$ apart.

Find the exact circular function value. - $\cos 2 \pi$