Question 1

Graph the function.
-$y=\cos \frac{1}{2} x$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Graph the function.
-$y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)$

Accepted Answer

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

Question 4

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
-Find $\cos \theta$.

Accepted Answer

A)  $\frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $- \frac { 5 } { 12 }$ 
D)  $- \frac { 12 } { 13 }$ 
A)  $\frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $- \frac { 5 } { 12 }$ 
D)  $- \frac { 12 } { 13 }$

Question 5

Convert the degree measure to radians. Leave answer as a multiple of π.
-$720 ^ { \circ }$

Accepted Answer

A)  $8 \pi$ 
B)  $4 \pi$ 
C)  $\frac { 9 \pi } { 2 }$ 
D)  $\frac { 7 \pi } { 2 }$ 
A)  $8 \pi$ 
B)  $4 \pi$ 
C)  $\frac { 9 \pi } { 2 }$ 
D)  $\frac { 7 \pi } { 2 }$

Question 6

Solve the problem.
-A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Accepted Answer

A)  $s ( t ) = - 6 \cos 2 \pi t$ 
B)  $s ( t ) = 6 \cos \frac { 1 } { 2 } t$ 
C)  $s ( t ) = 6 \cos 4 \pi t$ 
D)  $s ( t ) = - 6 \cos 4 \pi t$ 
A)  $s ( t ) = - 6 \cos 2 \pi t$ 
B)  $s ( t ) = 6 \cos \frac { 1 } { 2 } t$ 
C)  $s ( t ) = 6 \cos 4 \pi t$ 
D)  $s ( t ) = - 6 \cos 4 \pi t$

Question 7

Find the exact values of s in the given interval that satisfy the given condition.
-$[ 0,2 \pi ) ; \tan ^ { 2 } \mathrm {~s} = \frac { 1 } { 3 }$

Accepted Answer

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

Question 8

Give the amplitude or period as requested.
-Amplitude of $y = - 3 \cos \frac { 1 } { 2 } x$

Accepted Answer

A)  $\frac { \pi } { 3 }$ 
B)  $4 \pi$ 
C)  3 
D)  $\frac { 3 \pi } { 2 }$ 
A)  $\frac { \pi } { 3 }$ 
B)  $4 \pi$ 
C)  3 
D)  $\frac { 3 \pi } { 2 }$

Question 9

Solve the problem.
-Electrical wire is being wound around a drum with radius of $1.12$ meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of $317.5 ^ { \circ }$ ?

Accepted Answer

A)  $6.11 \mathrm {~m}$ 
B)  $6.31 \mathrm {~m}$ 
C)  $6.21 \mathrm {~m}$ 
D)  $6.01 \mathrm {~m}$ 
A)  $6.11 \mathrm {~m}$ 
B)  $6.31 \mathrm {~m}$ 
C)  $6.21 \mathrm {~m}$ 
D)  $6.01 \mathrm {~m}$

Question 10

Find the specified quantity.
-Find the period of $y = - 4 \cos \left( 5 x + \frac { \pi } { 2 } \right)$.

Accepted Answer

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

Question 11

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Is it correct to say that the value of } \tan 60 = \sqrt { 3 } \text { ? Explain your answer. }$$

Accepted Answer

No, it is not correct because

Question 12

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

Accepted Answer

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

Question 13

Solve the problem.
-A wheel with a 23-inch diameter is turning at the rate of 31 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Accepted Answer

A)  $2286 \mathrm { in } . / \mathrm { min }$ 
B)  $2247 \mathrm { in } . / \mathrm { min }$ 
C)  $2240 \mathrm { in } . / \mathrm { min }$ 
D)  $2293 \mathrm { in } . / \mathrm { min }$ 
A)  $2286 \mathrm { in } . / \mathrm { min }$ 
B)  $2247 \mathrm { in } . / \mathrm { min }$ 
C)  $2240 \mathrm { in } . / \mathrm { min }$ 
D)  $2293 \mathrm { in } . / \mathrm { min }$

Question 14

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place.
-$\mathrm { r } = 45.99 \mathrm { ft } ; \theta = \frac { \pi } { 30 }$ radians

Accepted Answer

A)  $14.4 \mathrm { ft }$ 
B)  $4.8 \mathrm { ft }$ 
C)  $2.4 \mathrm { ft }$ 
D)  $9.6 \mathrm { ft }$ 
A)  $14.4 \mathrm { ft }$ 
B)  $4.8 \mathrm { ft }$ 
C)  $2.4 \mathrm { ft }$ 
D)  $9.6 \mathrm { ft }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
-If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.
-

Accepted Answer

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

Question 17

Approximate the length using the formula for arc length. Round to the nearest meter.
-A tree $460 \mathrm {~m}$ away subtends an angle of $5 ^ { \circ }$. Find the height of the tree.

Accepted Answer

A)  $37 \mathrm {~m}$ 
B)  $80 \mathrm {~m}$ 
C)  $83 \mathrm {~m}$ 
D)  $40 \mathrm {~m}$ 
A)  $37 \mathrm {~m}$ 
B)  $80 \mathrm {~m}$ 
C)  $83 \mathrm {~m}$ 
D)  $40 \mathrm {~m}$

Question 18

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

A.
 
B.
 
C.
 
D.

Accepted Answer

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

Question 19

Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 2 \cos 3$ t inches after $t$ seconds. What are the frequency and period of the system?

Accepted Answer

A)  Frequency $= \frac { \pi } { 3 }$ cycles per sec, period $= \frac { 3 } { \pi } \sec$ 
B)  Frequency $= 3$ cycles per sec, period $= \frac { 1 } { 3 } \mathrm { sec }$ 
C)  Frequency $= \frac { 3 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 3 } \mathrm { sec }$ 
D)  Frequency $= \frac { 3 } { \pi }$ cycles per sec, period $= \frac { \pi } { 3 } \mathrm { sec }$ 
A)  Frequency $= \frac { \pi } { 3 }$ cycles per sec, period $= \frac { 3 } { \pi } \sec$ 
B)  Frequency $= 3$ cycles per sec, period $= \frac { 1 } { 3 } \mathrm { sec }$ 
C)  Frequency $= \frac { 3 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 3 } \mathrm { sec }$ 
D)  Frequency $= \frac { 3 } { \pi }$ cycles per sec, period $= \frac { \pi } { 3 } \mathrm { sec }$

Question 20

Use the formula $$\omega = \frac { \theta } { t }$$ to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\theta = \frac { \pi } { 2 }$ radian, $t = 13 \mathrm { sec }$

Accepted Answer

A)  $\frac { 13 \pi } { 2 }$ radians per sec 
B)  $\frac { \pi } { 26 }$ radian per sec 
C)  $\frac { 26 } { \pi }$ radians per sec 
D)  $\frac { 2 \pi } { 13 }$ radians per sec 
A)  $\frac { 13 \pi } { 2 }$ radians per sec 
B)  $\frac { \pi } { 26 }$ radian per sec 
C)  $\frac { 26 } { \pi }$ radians per sec 
D)  $\frac { 2 \pi } { 13 }$ radians per sec

Graph the function. - $y=\cos \frac{1}{2} x$ $Graph the function. - y=\cos \frac{1}{2} x$

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

Graph the function. - $y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)$

Convert the degree measure to radians. Leave answer as a multiple of π. - $720 ^ { \circ }$

Solve the problem. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } \mathrm {~s} = \frac { 1 } { 3 }$

Give the amplitude or period as requested. -Amplitude of $y = - 3 \cos \frac { 1 } { 2 } x$

Solve the problem. -Electrical wire is being wound around a drum with radius of $1.12$ meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of $317.5 ^ { \circ }$ ?

Find the specified quantity. -Find the period of $y = - 4 \cos \left( 5 x + \frac { \pi } { 2 } \right)$ .

Write the word or phrase that best completes each statement or answers the question. - $\text { Is it correct to say that the value of } \tan 60 = \sqrt { 3 } \text { ? Explain your answer. }$

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

Solve the problem. -A wheel with a 23-inch diameter is turning at the rate of 31 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 45.99 \mathrm { ft } ; \theta = \frac { \pi } { 30 }$ radians

Write the word or phrase that best completes each statement or answers the question. -If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree $460 \mathrm {~m}$ away subtends an angle of $5 ^ { \circ }$ . Find the height of the tree.

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 2 \cos 3$ t inches after $t$ seconds. What are the frequency and period of the system?

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\theta = \frac { \pi } { 2 }$ radian, $t = 13 \mathrm { sec }$

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

Graph the function. - y=cos⁡12xy=\cos \frac{1}{2} xy=cos21​x

Find the exact value of s in the given interval that has the given circular function value. - [3π2,2π];tan⁡s=−33\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \tan \mathrm { s } = - \frac { \sqrt { 3 } } { 3 }[23π​,2π];tans=−33​​

Graph the function. - y=23csc⁡(54x+π5)y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)y=32​csc(45​x+5π​)

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find cos⁡θ\cos \thetacosθ .

Convert the degree measure to radians. Leave answer as a multiple of π. - 720∘720 ^ { \circ }720∘

Solve the problem. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is 12\frac { 1 } { 2 }21​ second, determine a trigonometric model that gives the position of the weight at time ttt seconds.

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);tan⁡2 s=13[ 0,2 \pi ) ; \tan ^ { 2 } \mathrm {~s} = \frac { 1 } { 3 }[0,2π);tan2 s=31​

Give the amplitude or period as requested. -Amplitude of y=−3cos⁡12xy = - 3 \cos \frac { 1 } { 2 } xy=−3cos21​x

Solve the problem. -Electrical wire is being wound around a drum with radius of 1.121.121.12 meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of 317.5∘317.5 ^ { \circ }317.5∘ ?

Find the specified quantity. -Find the period of y=−4cos⁡(5x+π2)y = - 4 \cos \left( 5 x + \frac { \pi } { 2 } \right)y=−4cos(5x+2π​) .

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

Solve the problem. -A wheel with a 23-inch diameter is turning at the rate of 31 revolutions per minute. To the nearest inch, what is the speed of a point on the rim in in./min?

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - r=45.99ft;θ=π30\mathrm { r } = 45.99 \mathrm { ft } ; \theta = \frac { \pi } { 30 }r=45.99ft;θ=30π​ radians

Write the word or phrase that best completes each statement or answers the question. -If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree 460 m460 \mathrm {~m}460 m away subtends an angle of 5∘5 ^ { \circ }5∘ . Find the height of the tree.

Match the function with its graph. -1) y=2+sin⁡xy = 2 + \sin xy=2+sinx 2) y=2+cos⁡xy = 2 + \cos xy=2+cosx 3) y=−2+sin⁡xy = - 2 + \sin xy=−2+sinx 4) y=−2+cos⁡xy = - 2 + \cos xy=−2+cosx A. B. C. D.

Solve the problem. -The position of a weight attached to a spring is s(t)=−2cos⁡3s ( t ) = - 2 \cos 3s(t)=−2cos3 t inches after ttt seconds. What are the frequency and period of the system?

Use the formula ω=θt\omega = \frac { \theta } { t }ω=tθ​ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - θ=π2\theta = \frac { \pi } { 2 }θ=2π​ radian, t=13sect = 13 \mathrm { sec }t=13sec

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

Graph the function. - $y=\cos \frac{1}{2} x$ $Graph the function. - y=\cos \frac{1}{2} x$

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

Graph the function. - $y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{2}{3} \csc \left(\frac{5}{4} x+\frac{\pi}{5}\right)$

Convert the degree measure to radians. Leave answer as a multiple of π. - $720 ^ { \circ }$

Solve the problem. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } \mathrm {~s} = \frac { 1 } { 3 }$

Give the amplitude or period as requested. -Amplitude of $y = - 3 \cos \frac { 1 } { 2 } x$

Solve the problem. -Electrical wire is being wound around a drum with radius of $1.12$ meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of $317.5 ^ { \circ }$ ?

Find the specified quantity. -Find the period of $y = - 4 \cos \left( 5 x + \frac { \pi } { 2 } \right)$ .

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

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 45.99 \mathrm { ft } ; \theta = \frac { \pi } { 30 }$ radians

Approximate the length using the formula for arc length. Round to the nearest meter. -A tree $460 \mathrm {~m}$ away subtends an angle of $5 ^ { \circ }$ . Find the height of the tree.

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 2 \cos 3$ t inches after $t$ seconds. What are the frequency and period of the system?

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\theta = \frac { \pi } { 2 }$ radian, $t = 13 \mathrm { sec }$