Question 1

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

Question 2

Find the specified quantity.
-Find the amplitude of $y = - 3 \cos ( 2 x - \pi )$.

Accepted Answer

A)  2 
B)  $\pi$ 
C)  3 
D)  $- 6$ 
A)  2 
B)  $\pi$ 
C)  3 
D)  $- 6$

Question 3

Provide an appropriate response.
-Describe how an angle measure can be converted from degrees to radians.

Accepted Answer

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

Question 4

Solve the problem.
-A pulley of radius $5 \mathrm {~cm}$ rotates 19 times in $64 \mathrm { sec }$. Find the angular speed of the pulley.

Accepted Answer

A)  $\frac { 32 \pi } { 95 }$ radian per sec 
B)  $\frac { 95 \pi } { 32 }$ radians per sec 
C)  $\frac { 95 \pi } { 64 }$ radians per sec 
D)  $\frac { 64 \pi } { 95 }$ radian per sec 
A)  $\frac { 32 \pi } { 95 }$ radian per sec 
B)  $\frac { 95 \pi } { 32 }$ radians per sec 
C)  $\frac { 95 \pi } { 64 }$ radians per sec 
D)  $\frac { 64 \pi } { 95 }$ radian per sec

Question 5

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$$- \frac { \pi } { 5 }$$

Accepted Answer

A)  $- 0.63 ^ { \circ }$ 
B)  $- 36 ^ { \circ }$ 
C)  $- \frac { \pi } { 5 } \circ$ 
D)  $- 36 \pi ^ { \circ }$ 
A)  $- 0.63 ^ { \circ }$ 
B)  $- 36 ^ { \circ }$ 
C)  $- \frac { \pi } { 5 } \circ$ 
D)  $- 36 \pi ^ { \circ }$

Question 6

Find the exact values of s in the given interval that satisfy the given condition.
-$[ 0,2 \pi ) ; 4 \sin ^ { 2 } \mathrm {~s} = 3$

Accepted Answer

A)  $\frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
B)  $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
C)  $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $\frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }$ 
A)  $\frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$ 
B)  $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
C)  $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $\frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }$

Question 7

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$\frac { 4 \pi } { 7 }$

Accepted Answer

A)  $103.86 ^ { \circ }$ 
B)  $103.36 ^ { \circ }$ 
C)  $102.86 ^ { \circ }$ 
D)  $102.36 ^ { \circ }$ 
A)  $103.86 ^ { \circ }$ 
B)  $103.36 ^ { \circ }$ 
C)  $102.86 ^ { \circ }$ 
D)  $102.36 ^ { \circ }$

Question 8

Convert the degree measure to radians. Leave answer as a multiple of π.
-$- 430 ^ { \circ }$

Accepted Answer

A)  $- \frac { 43 \pi } { 18 }$ 
B)  $- \frac { 43 \pi } { 36 }$ 
C)  $- \frac { 43 \pi } { 9 }$ 
D)  $- \frac { 7 \pi } { 18 }$ 
A)  $- \frac { 43 \pi } { 18 }$ 
B)  $- \frac { 43 \pi } { 36 }$ 
C)  $- \frac { 43 \pi } { 9 }$ 
D)  $- \frac { 7 \pi } { 18 }$

Question 9

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

Accepted Answer

A)  $s = \frac { \pi } { 6 }$ 
B)  $\mathrm { s } = \frac { 3 \pi } { 4 }$ 
C)  $\mathrm { s } = \frac { 2 \pi } { 3 }$ 
D)  $s = \frac { 5 \pi } { 6 }$ 
A)  $s = \frac { \pi } { 6 }$ 
B)  $\mathrm { s } = \frac { 3 \pi } { 4 }$ 
C)  $\mathrm { s } = \frac { 2 \pi } { 3 }$ 
D)  $s = \frac { 5 \pi } { 6 }$

Question 10

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

Accepted Answer

A)  $\cos \left( x - \frac { \pi } { 3 } \right)$ 
B)  $\sin \left( x - \frac { \pi } { 3 } \right)$ 
C)  $\cos x - \frac { \pi } { 3 }$ 
D)  $\cos \left( x - \frac { \pi } { 6 } \right)$ 
A)  $\cos \left( x - \frac { \pi } { 3 } \right)$ 
B)  $\sin \left( x - \frac { \pi } { 3 } \right)$ 
C)  $\cos x - \frac { \pi } { 3 }$ 
D)  $\cos \left( x - \frac { \pi } { 6 } \right)$

Question 11

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.
-

Accepted Answer

A)  $y = \tan 4 x$ 
B)  $y = 4 \tan x$ 
C)  $y = 4 \cot x$ 
D)  $y = \cot 4 x$ 
A)  $y = \tan 4 x$ 
B)  $y = 4 \tan x$ 
C)  $y = 4 \cot x$ 
D)  $y = \cot 4 x$

Question 12

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Is it correct to say that the value of } \cos 45 = \frac { \sqrt { 2 } } { 2 } \text { ? Explain your answer. }$$

Accepted Answer

No, it is not correct because

Question 13

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

Accepted Answer

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

Question 14

Solve the problem.
-A wheel is rotating at 3 radians/sec, and the wheel has a 44 -inch diameter. To the nearest foot, what is the speed of a point on the rim in $\mathrm { ft } / \mathrm { min }$ ?

Accepted Answer

A)  $330 \mathrm { ft } / \mathrm { min }$ 
B)  $325 \mathrm { ft } / \mathrm { min }$ 
C)  $320 \mathrm { ft } / \mathrm { min }$ 
D)  $335 \mathrm { ft } / \mathrm { min }$ 
A)  $330 \mathrm { ft } / \mathrm { min }$ 
B)  $325 \mathrm { ft } / \mathrm { min }$ 
C)  $320 \mathrm { ft } / \mathrm { min }$ 
D)  $335 \mathrm { ft } / \mathrm { min }$

Question 15

Give the amplitude or period as requested.
-Period of $y = 3 \cos \frac { 1 } { 4 } x$

Accepted Answer

A)  3 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $8 \pi$ 
D)  $\frac { \pi } { 4 }$ 
A)  3 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $8 \pi$ 
D)  $\frac { \pi } { 4 }$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Solve the problem.
-A bicycle with a 24-inch wheel (diameter) travels a distance of 1000 feet. How many revolutions does the wheel make (to the nearest revolution)?

Accepted Answer

A)  159 revolutions 
B)  153 revolutions 
C)  312 revolutions 
D)  318 revolutions 
A)  159 revolutions 
B)  153 revolutions 
C)  312 revolutions 
D)  318 revolutions

Question 19

Graph the function.
-$y=-1+\sin \left(x+\frac{\pi}{2}\right)$

Accepted Answer

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

Question 20

Graph the function.
-$y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)$

Accepted Answer

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

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

Find the specified quantity. -Find the amplitude of $y = - 3 \cos ( 2 x - \pi )$ .

Provide an appropriate response. -Describe how an angle measure can be converted from degrees to radians.

Solve the problem. -A pulley of radius $5 \mathrm {~cm}$ rotates 19 times in $64 \mathrm { sec }$ . Find the angular speed of the pulley.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 5 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; 4 \sin ^ { 2 } \mathrm {~s} = 3$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 4 \pi } { 7 }$

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 430 ^ { \circ }$

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

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

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. -

Write the word or phrase that best completes each statement or answers the question. - $\text { Is it correct to say that the value of } \cos 45 = \frac { \sqrt { 2 } } { 2 } \text { ? Explain your answer. }$

Solve the problem. -A wheel is rotating at 3 radians/sec, and the wheel has a 44 -inch diameter. To the nearest foot, what is the speed of a point on the rim in $\mathrm { ft } / \mathrm { min }$ ?

Give the amplitude or period as requested. -Period of $y = 3 \cos \frac { 1 } { 4 } x$

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

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

Solve the problem. -A bicycle with a 24-inch wheel (diameter) travels a distance of 1000 feet. How many revolutions does the wheel make (to the nearest revolution)?

Graph the function. - $y=-1+\sin \left(x+\frac{\pi}{2}\right)$ $Graph the function. - y=-1+\sin \left(x+\frac{\pi}{2}\right)$

Graph the function. - $y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)$

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

Review of Basic Concepts

Filters

Exam 6: The Circular Functions and Their Graphs

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​)

Find the specified quantity. -Find the amplitude of y=−3cos⁡(2x−π)y = - 3 \cos ( 2 x - \pi )y=−3cos(2x−π) .

Provide an appropriate response. -Describe how an angle measure can be converted from degrees to radians.

Solve the problem. -A pulley of radius 5 cm5 \mathrm {~cm}5 cm rotates 19 times in 64sec64 \mathrm { sec }64sec . Find the angular speed of the pulley.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −π5- \frac { \pi } { 5 }−5π​

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);4sin⁡2 s=3[ 0,2 \pi ) ; 4 \sin ^ { 2 } \mathrm {~s} = 3[0,2π);4sin2 s=3

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 4π7\frac { 4 \pi } { 7 }74π​

Convert the degree measure to radians. Leave answer as a multiple of π. - −430∘- 430 ^ { \circ }−430∘

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

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

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. -

Solve the problem. -A wheel is rotating at 3 radians/sec, and the wheel has a 44 -inch diameter. To the nearest foot, what is the speed of a point on the rim in ft/min\mathrm { ft } / \mathrm { min }ft/min ?

Give the amplitude or period as requested. -Period of y=3cos⁡14xy = 3 \cos \frac { 1 } { 4 } xy=3cos41​x

Graph the function over a one-period interval. - y=14cos⁡2(x+π4)y=\frac{1}{4} \cos 2\left(x+\frac{\pi}{4}\right)y=41​cos2(x+4π​)

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

Solve the problem. -A bicycle with a 24-inch wheel (diameter) travels a distance of 1000 feet. How many revolutions does the wheel make (to the nearest revolution)?

Graph the function. - y=−1+sin⁡(x+π2)y=-1+\sin \left(x+\frac{\pi}{2}\right)y=−1+sin(x+2π​)

Graph the function. - y=23cot⁡(56x+π3)y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)y=32​cot(65​x+3π​)

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

Review of Basic Concepts

Filters

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

Find the specified quantity. -Find the amplitude of $y = - 3 \cos ( 2 x - \pi )$ .

Solve the problem. -A pulley of radius $5 \mathrm {~cm}$ rotates 19 times in $64 \mathrm { sec }$ . Find the angular speed of the pulley.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 5 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; 4 \sin ^ { 2 } \mathrm {~s} = 3$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 4 \pi } { 7 }$

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 430 ^ { \circ }$

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

Solve the problem. -A wheel is rotating at 3 radians/sec, and the wheel has a 44 -inch diameter. To the nearest foot, what is the speed of a point on the rim in $\mathrm { ft } / \mathrm { min }$ ?

Give the amplitude or period as requested. -Period of $y = 3 \cos \frac { 1 } { 4 } x$

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

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

Graph the function. - $y=-1+\sin \left(x+\frac{\pi}{2}\right)$ $Graph the function. - y=-1+\sin \left(x+\frac{\pi}{2}\right)$

Graph the function. - $y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{2}{3} \cot \left(\frac{5}{6} x+\frac{\pi}{3}\right)$