Question 1

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π.
-$$- 1.4194$$

Accepted Answer

A)  $- 80.83 ^ { \circ }$ 
B)  $- 82.03 ^ { \circ }$ 
C)  $- 80.33 ^ { \circ }$ 
D)  $- 81.33 ^ { \circ }$ 
A)  $- 80.83 ^ { \circ }$ 
B)  $- 82.03 ^ { \circ }$ 
C)  $- 80.33 ^ { \circ }$ 
D)  $- 81.33 ^ { \circ }$

Question 2

Solve the problem.
-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, $\mathrm { A } = 7900$, and $B = 2500$. Determine the month with the greatest total sales and give the sales in that month.

Accepted Answer

A)  June; $\$ 7900$ 
B)  December; $\$ 10,400$ 
C)  March; $\$ 10,400$ 
D)  September; $\$ 5400$ 
A)  June; $\$ 7900$ 
B)  December; $\$ 10,400$ 
C)  March; $\$ 10,400$ 
D)  September; $\$ 5400$

Question 3

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

Accepted Answer

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

Question 4

Find the phase shift of the function.
-$$y = - 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 4 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $\frac { \pi } { 16 }$ units to the right 
D)  $\pi$ units to the left 
A)  $\frac { \pi } { 4 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $\frac { \pi } { 16 }$ units to the right 
D)  $\pi$ units to the left

Question 5

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec }$

Accepted Answer

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

Question 6

Solve the problem.
-Find $\omega$ for a spoke on a bike tire revolving 80 times per minute.

Accepted Answer

A)  $\frac { \pi } { 80 }$ radians per min 
B)  $\frac { \pi } { 160 }$ radians per min 
C)  $80 \pi$ radians per min 
D)  $160 \pi$ radians per min 
A)  $\frac { \pi } { 80 }$ radians per min 
B)  $\frac { \pi } { 160 }$ radians per min 
C)  $80 \pi$ radians per min 
D)  $160 \pi$ radians per min

Question 7

Graph the function.
-$y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)$

Accepted Answer

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

Question 8

Solve the problem.
-For an electrical circuit, the voltage $E$ is modeled by $\mathrm { E } = 2.7 \cos 30 \pi \mathrm { t }$, where $t$ is the time in seconds. How many cycles are completed in one second?

Accepted Answer

A)  $30 \pi$ cycles 
B)  $2.7$ cycles 
C)  30 cycles 
D)  15 cycles 
A)  $30 \pi$ cycles 
B)  $2.7$ cycles 
C)  30 cycles 
D)  15 cycles

Question 9

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 10

Graph the function.
-$y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)$

Accepted Answer

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

Question 11

Solve the problem.
-What is the difference in area covered by a single 1 -inch windshield wiper operating with a central angle of $125 ^ { \circ }$ compared to a pair of 9 -inch wipers operating together each having a central angle of $119 ^ { \circ }$ ? Round to the nearest hundredth.

Accepted Answer

A)  $172.14 \mathrm { in } ^ { 2 }$ 
B)  $167.14 \mathrm { in. } ^ { 2 }$ 
C)  $169.32 \mathrm { in. } { } ^ { 2 }$ 
D)  $83.03 \mathrm { in } { } ^ { 2 }$ 
A)  $172.14 \mathrm { in } ^ { 2 }$ 
B)  $167.14 \mathrm { in. } ^ { 2 }$ 
C)  $169.32 \mathrm { in. } { } ^ { 2 }$ 
D)  $83.03 \mathrm { in } { } ^ { 2 }$

Question 12

Solve the problem.
-Let angle $P O Q$ be designated $\theta$. Angles $P Q R$ and $V R Q$ are right angles. If $\theta = 45 ^ { \circ }$, find the exact length of $O Q$.

Accepted Answer

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

Question 13

Find the specified quantity.
-Find the amplitude of $y = 3 \sin ( 4 x + \pi )$.

Accepted Answer

A)  $\pi$ 
B)  4 
C)  3 
D)  12 
A)  $\pi$ 
B)  4 
C)  3 
D)  12

Question 14

Solve the problem.
-A coil of wire rotating in a magnetic field induces a voltage given by $\mathrm { e } = 20 \sin \left( \frac { \pi \mathrm { t } } { 4 } - \frac { \pi } { 2 } \right)$
where $t$ is time in seconds. Find the smallest positive time to produce a voltage of $10 \sqrt { 2 }$.

Accepted Answer

A)  $3 \mathrm { sec }$ 
B)  $2.8 \pi \mathrm { sec }$ 
C)  $3 \pi \mathrm { sec }$ 
D)  $2.8 \mathrm { sec }$ 
A)  $3 \mathrm { sec }$ 
B)  $2.8 \pi \mathrm { sec }$ 
C)  $3 \pi \mathrm { sec }$ 
D)  $2.8 \mathrm { sec }$

Question 15

Solve the problem.
-Let angle $P O Q$ be designated $\theta$. Angles $P Q R$ and VRQ are right angles. If $\theta = 74 ^ { \circ }$, find the length of VR accurate to four decimal places.

Accepted Answer

A)  $3.4874$ 
B)  $0.2867$ 
C)  $0.2756$ 
D)  $0.9613$ 
A)  $3.4874$ 
B)  $0.2867$ 
C)  $0.2756$ 
D)  $0.9613$

Question 16

Solve the problem.
-Find $v$ for the tip of the hour hand of a clock, if the hand is $17 \mathrm {~cm}$ long.

Accepted Answer

A)  $102 \pi \mathrm { cm }$ per hour 
B)  $\frac { 17 \pi } { 3 } \mathrm {~cm}$ per hour 
C)  $\frac { 17 \pi } { 6 } \mathrm {~cm}$ per hour 
D)  $\frac { 17 \pi } { 12 } \mathrm {~cm}$ per hour 
A)  $102 \pi \mathrm { cm }$ per hour 
B)  $\frac { 17 \pi } { 3 } \mathrm {~cm}$ per hour 
C)  $\frac { 17 \pi } { 6 } \mathrm {~cm}$ per hour 
D)  $\frac { 17 \pi } { 12 } \mathrm {~cm}$ per hour

Question 17

Determine the equation of the graph.
-

Accepted Answer

A)  $y = - 4 + \sec 4 x$ 
B)  $y = - 4 + \csc x$ 
C)  $y = - 4 - \csc x$ 
D)  $y = - 4 + \sec x$ 
A)  $y = - 4 + \sec 4 x$ 
B)  $y = - 4 + \csc x$ 
C)  $y = - 4 - \csc x$ 
D)  $y = - 4 + \sec x$

Question 18

Find the exact circular function value.
-$\cot \pi$

Accepted Answer

A)  1 
B)  0 
C)  undefined 
D)  $- 1$ 
A)  1 
B)  0 
C)  undefined 
D)  $- 1$

Question 19

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$74.80 ^ { \circ }$

Accepted Answer

A)  $1.1055$ 
B)  $1.3055$ 
C)  $1.4055$ 
D)  $1.2055$ 
A)  $1.1055$ 
B)  $1.3055$ 
C)  $1.4055$ 
D)  $1.2055$

Question 20

Solve the problem.
-A circular sector has an area of 17 in $^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.

Accepted Answer

A)  $30 ^ { \circ }$ 
B)  $8 ^ { \circ }$ 
C)  $15 ^ { \circ }$ 
D)  $5 ^ { \circ }$ 
A)  $30 ^ { \circ }$ 
B)  $8 ^ { \circ }$ 
C)  $15 ^ { \circ }$ 
D)  $5 ^ { \circ }$

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π. - $- 1.4194$

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

Find the phase shift of the function. - $y = - 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec }$

Solve the problem. -Find $\omega$ for a spoke on a bike tire revolving 80 times per minute.

Graph the function. - $y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)$

Solve the problem. -For an electrical circuit, the voltage $E$ is modeled by $\mathrm { E } = 2.7 \cos 30 \pi \mathrm { t }$ , where $t$ is the time in seconds. How many cycles are completed in one second?

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

Graph the function. - $y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)$

Solve the problem. -What is the difference in area covered by a single 1 -inch windshield wiper operating with a central angle of $125 ^ { \circ }$ compared to a pair of 9 -inch wipers operating together each having a central angle of $119 ^ { \circ }$ ? Round to the nearest hundredth.

Find the specified quantity. -Find the amplitude of $y = 3 \sin ( 4 x + \pi )$ .

Solve the problem. -A coil of wire rotating in a magnetic field induces a voltage given by $\mathrm { e } = 20 \sin \left( \frac { \pi \mathrm { t } } { 4 } - \frac { \pi } { 2 } \right)$ where $t$ is time in seconds. Find the smallest positive time to produce a voltage of $10 \sqrt { 2 }$ .

Solve the problem. -Find $v$ for the tip of the hour hand of a clock, if the hand is $17 \mathrm {~cm}$ long.

Determine the equation of the graph. -

Find the exact circular function value. - $\cot \pi$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $74.80 ^ { \circ }$

Solve the problem. -A circular sector has an area of 17 in $^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.

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

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Exam 6: The Circular Functions and Their Graphs

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π. - −1.4194- 1.4194−1.4194

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

Find the phase shift of the function. - y=−3cos⁡(14x+π4)y = - 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)y=−3cos(41​x+4π​)

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - r=2 cm,ω=π3\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 3 }r=2 cm,ω=3π​ radian per sec\mathrm { sec }sec

Solve the problem. -Find ω\omegaω for a spoke on a bike tire revolving 80 times per minute.

Graph the function. - y=13cot⁡(35x−π3)y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)y=31​cot(53​x−3π​)

Solve the problem. -For an electrical circuit, the voltage EEE is modeled by E=2.7cos⁡30πt\mathrm { E } = 2.7 \cos 30 \pi \mathrm { t }E=2.7cos30πt , where ttt is the time in seconds. How many cycles are completed in one second?

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​)

Graph the function. - y=56tan⁡(12x−π4)y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)y=65​tan(21​x−4π​)

Solve the problem. -Let angle POQP O QPOQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQV R QVRQ are right angles. If θ=45∘\theta = 45 ^ { \circ }θ=45∘ , find the exact length of OQO QOQ .

Find the specified quantity. -Find the amplitude of y=3sin⁡(4x+π)y = 3 \sin ( 4 x + \pi )y=3sin(4x+π) .

Solve the problem. -Let angle POQP O QPOQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=74∘\theta = 74 ^ { \circ }θ=74∘ , find the length of VR accurate to four decimal places.

Solve the problem. -Find vvv for the tip of the hour hand of a clock, if the hand is 17 cm17 \mathrm {~cm}17 cm long.

Determine the equation of the graph. -

Find the exact circular function value. - cot⁡π\cot \picotπ

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 74.80∘74.80 ^ { \circ }74.80∘

Solve the problem. -A circular sector has an area of 17 in 2^ { 2 }2 and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.

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

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π. - $- 1.4194$

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

Find the phase shift of the function. - $y = - 3 \cos \left( \frac { 1 } { 4 } x + \frac { \pi } { 4 } \right)$

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec }$

Solve the problem. -Find $\omega$ for a spoke on a bike tire revolving 80 times per minute.

Graph the function. - $y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)$ $Graph the function. - y=\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{3}\right)$

Solve the problem. -For an electrical circuit, the voltage $E$ is modeled by $\mathrm { E } = 2.7 \cos 30 \pi \mathrm { t }$ , where $t$ is the time in seconds. How many cycles are completed in one second?

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

Graph the function. - $y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{5}{6} \tan \left(\frac{1}{2} x-\frac{\pi}{4}\right)$

Find the specified quantity. -Find the amplitude of $y = 3 \sin ( 4 x + \pi )$ .

Solve the problem. -Find $v$ for the tip of the hour hand of a clock, if the hand is $17 \mathrm {~cm}$ long.

Find the exact circular function value. - $\cot \pi$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $74.80 ^ { \circ }$

Solve the problem. -A circular sector has an area of 17 in $^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.