Question 1

Draw the angle.
-$330 ^ { \circ }$

Accepted Answer

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

Question 2

Solve the problem.
-An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of $\frac { 1 } { 3 }$ radian is swept out, what is the linear speed of the object?

Accepted Answer

A)  $\frac { 1 } { 6 }$ radians/sec 
B)  $6 \mathrm {~cm} / \mathrm { sec }$ 
C)  6 radians/sec 
D)  $\frac { 1 } { 6 } \mathrm {~cm} / \mathrm { sec }$ 
A)  $\frac { 1 } { 6 }$ radians/sec 
B)  $6 \mathrm {~cm} / \mathrm { sec }$ 
C)  6 radians/sec 
D)  $\frac { 1 } { 6 } \mathrm {~cm} / \mathrm { sec }$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\sin \left( - 60 ^ { \circ } \right)$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 2 }$

Question 4

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator.
-$\sec ^ { 2 } 40 ^ { \circ } - \tan ^ { 2 } 40 ^ { \circ }$

Accepted Answer

A)  0 
B)  2 
C)  1 
D)  $- 1$ 
A)  0 
B)  2 
C)  1 
D)  $- 1$

Question 5

Convert the angle to D° M' S'' form. Round the answer to the nearest second.
-$64.64 ^ { \circ }$

Accepted Answer

A)  $64 ^ { \circ } 38 ^ { \prime } 30 ^ { \prime \prime }$ 
B)  $64 ^ { \circ } 38 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $64 ^ { \circ } 38 ^ { \prime } 64 ^ { \prime \prime }$ 
D)  $64 ^ { \circ } 38 ^ { \prime } 24 ^ { \prime \prime }$ 
A)  $64 ^ { \circ } 38 ^ { \prime } 30 ^ { \prime \prime }$ 
B)  $64 ^ { \circ } 38 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $64 ^ { \circ } 38 ^ { \prime } 64 ^ { \prime \prime }$ 
D)  $64 ^ { \circ } 38 ^ { \prime } 24 ^ { \prime \prime }$

Question 6

Solve the problem.
-If $\sin \theta = \frac { 1 } { 9 }$, find $\csc \theta$

Accepted Answer

A)  $- \frac { 1 } { 9 }$ 
B)  9 
C)  $\frac { 8 } { 9 }$ 
D)  undefined 
A)  $- \frac { 1 } { 9 }$ 
B)  9 
C)  $\frac { 8 } { 9 }$ 
D)  undefined

Question 7

Write the word or phrase that best completes each statement or answers the question.
-The data below represent the average monthly cost of natural gas in an Oregon home. $$\begin{array}{l}
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \
\hline \text { Cost } & 18.90 & 24.24 & 44.58 & 68.25 & 91.92 & 109.26
\end{array}\\
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \
\hline \text { Cost } & 113.60 & 106.26 & 91.92 & 68.25 & 42.58 & 24.24
\end{array}
\end{array}$$   Above is the graph of 47.35 sin x. Make a scatter diagram of the data. Find the sinusoidal function of the form
y = A sin (ωx - Φ) + B which fits the data.

Accepted Answer

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

Question 8

Choose the one alternative that best completes the statement or answers the question.
-If $\sin \theta = 0.3$, find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$.

Accepted Answer

A)  $0.9 + 6 \pi$ 
B)  $2.9$ 
C)  $0.9$ 
D)  $0.3$ 
A)  $0.9 + 6 \pi$ 
B)  $2.9$ 
C)  $0.9$ 
D)  $0.3$

Question 9

Find the exact value. Do not use a calculator.
-$\cot \frac { \pi } { 6 }$

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  1 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $\sqrt { 3 }$ 
A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  1 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $\sqrt { 3 }$

Question 10

Find the exact value. Do not use a calculator.
-$$\cos \frac { 20 \pi } { 3 }$$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 11

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

Accepted Answer

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

Question 12

Choose the one alternative that best completes the statement or answers the question.
Use transformations to graph the function.
-$y=5 \sin x+1$

Accepted Answer

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

Question 13

Solve the problem.
-A gear with a radius of 16 centimeters is turning at $\frac { \pi } { 11 }$ radians/sec. What is the linear speed at a point on the outer edge of the gear?

Accepted Answer

A)  $\frac { 11 \pi } { 16 } \mathrm {~cm} / \mathrm { sec }$ 
B)  $\frac { \pi } { 176 } \mathrm {~cm} / \mathrm { sec }$ 
C)  $176 \pi \mathrm { cm } / \mathrm { sec }$ 
D)  $\frac { 16 \pi } { 11 } \mathrm {~cm} / \mathrm { sec }$ 
A)  $\frac { 11 \pi } { 16 } \mathrm {~cm} / \mathrm { sec }$ 
B)  $\frac { \pi } { 176 } \mathrm {~cm} / \mathrm { sec }$ 
C)  $176 \pi \mathrm { cm } / \mathrm { sec }$ 
D)  $\frac { 16 \pi } { 11 } \mathrm {~cm} / \mathrm { sec }$

Question 14

Solve the problem.
-If $\sin \theta = 0.7$, find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$.

Accepted Answer

A)  $0.7$ 
B)  $2.1$ 
C)  $2.1 + 6 \pi$ 
D)  $4.1$ 
A)  $0.7$ 
B)  $2.1$ 
C)  $2.1 + 6 \pi$ 
D)  $4.1$

Question 15

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

Accepted Answer

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

Question 16

Write the equation of a sine function that has the given characteristics.
-Amplitude: 3
Period: $5 \pi$
Phase Shift: $- \frac { \pi } { 5 }$

Accepted Answer

A)  $y = 3 \sin \left( \frac { 2 } { 5 } x + \frac { 2 } { 25 } \pi \right)$ 
B)  $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { 2 } { 25 } \pi \right)$ 
C)  $y = 3 \sin \left( \frac { 5 } { 2 } x - \frac { 2 } { 25 } \pi \right)$ 
D)  $y = 3 \sin \left( 6 x - \frac { \pi } { 6 } \right)$ 
A)  $y = 3 \sin \left( \frac { 2 } { 5 } x + \frac { 2 } { 25 } \pi \right)$ 
B)  $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { 2 } { 25 } \pi \right)$ 
C)  $y = 3 \sin \left( \frac { 5 } { 2 } x - \frac { 2 } { 25 } \pi \right)$ 
D)  $y = 3 \sin \left( 6 x - \frac { \pi } { 6 } \right)$

Question 17

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

Accepted Answer

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

Question 18

Convert the angle in radians to degrees.
-$\frac { 7 \pi } { 12 }$

Accepted Answer

A)  $154 ^ { \circ }$ 
B)  $309 \pi ^ { \circ }$ 
C)  $105 ^ { \circ }$ 
D)  $210 ^ { \circ }$ 
A)  $154 ^ { \circ }$ 
B)  $309 \pi ^ { \circ }$ 
C)  $105 ^ { \circ }$ 
D)  $210 ^ { \circ }$

Question 19

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places.
-$353 ^ { \circ }$

Accepted Answer

A)  $6.13$ 
B)  $6.14$ 
C)  $6.16$ 
D)  $6.15$ 
A)  $6.13$ 
B)  $6.14$ 
C)  $6.16$ 
D)  $6.15$

Question 20

Solve the problem.
-The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The restoring force F, in Newtons, acting on a string pendulum is given by the formula
F = mg sinθ
Where m is the mass in kilograms of the pendulum's bob, g =9.8 meters per second per second is the acceleration
Due to gravity, and θ is angle at which the pendulum is displaced from the perpendicular. What is the value of
The restoring force when m = 0.7 kilogram and θ = 45°? If necessary, round the answer to the nearest tenth of a
Newton.

Accepted Answer

A)  4.7 N 
B)  4.6 N 
C)  5.8 N 
D)  4.9 N 
A)  4.7 N 
B)  4.6 N 
C)  5.8 N 
D)  4.9 N

Draw the angle. - $330 ^ { \circ }$

Solve the problem. -An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of $\frac { 1 } { 3 }$ radian is swept out, what is the linear speed of the object?

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 60 ^ { \circ } \right)$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\sec ^ { 2 } 40 ^ { \circ } - \tan ^ { 2 } 40 ^ { \circ }$

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $64.64 ^ { \circ }$

Solve the problem. -If $\sin \theta = \frac { 1 } { 9 }$ , find $\csc \theta$

Choose the one alternative that best completes the statement or answers the question. -If $\sin \theta = 0.3$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

Find the exact value. Do not use a calculator. - $\cot \frac { \pi } { 6 }$

Find the exact value. Do not use a calculator. - $\cos \frac { 20 \pi } { 3 }$

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

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=5 \sin x+1$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=5 \sin x+1$

Solve the problem. -A gear with a radius of 16 centimeters is turning at $\frac { \pi } { 11 }$ radians/sec. What is the linear speed at a point on the outer edge of the gear?

Solve the problem. -If $\sin \theta = 0.7$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $5 \pi$ Phase Shift: $- \frac { \pi } { 5 }$

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

Convert the angle in radians to degrees. - $\frac { 7 \pi } { 12 }$

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $353 ^ { \circ }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 5: Trigonometric Functions

Draw the angle. - 330∘330 ^ { \circ }330∘

Solve the problem. -An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of 13\frac { 1 } { 3 }31​ radian is swept out, what is the linear speed of the object?

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - sin⁡(−60∘)\sin \left( - 60 ^ { \circ } \right)sin(−60∘)

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - sec⁡240∘−tan⁡240∘\sec ^ { 2 } 40 ^ { \circ } - \tan ^ { 2 } 40 ^ { \circ }sec240∘−tan240∘

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - 64.64∘64.64 ^ { \circ }64.64∘

Solve the problem. -If sin⁡θ=19\sin \theta = \frac { 1 } { 9 }sinθ=91​ , find csc⁡θ\csc \thetacscθ

Choose the one alternative that best completes the statement or answers the question. -If sin⁡θ=0.3\sin \theta = 0.3sinθ=0.3 , find the value of sin⁡θ+sin⁡(θ+2π)+sin⁡(θ+4π)\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )sinθ+sin(θ+2π)+sin(θ+4π) .

Find the exact value. Do not use a calculator. - cot⁡π6\cot \frac { \pi } { 6 }cot6π​

Find the exact value. Do not use a calculator. - cos⁡20π3\cos \frac { 20 \pi } { 3 }cos320π​

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

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=5sin⁡x+1y=5 \sin x+1y=5sinx+1

Solve the problem. -A gear with a radius of 16 centimeters is turning at π11\frac { \pi } { 11 }11π​ radians/sec. What is the linear speed at a point on the outer edge of the gear?

Solve the problem. -If sin⁡θ=0.7\sin \theta = 0.7sinθ=0.7 , find the value of sin⁡θ+sin⁡(θ+2π)+sin⁡(θ+4π)\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )sinθ+sin(θ+2π)+sin(θ+4π) .

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: 5π5 \pi5π Phase Shift: −π5- \frac { \pi } { 5 }−5π​

Find the phase shift of the function. - y=−2cos⁡(x+π4)y = - 2 \cos \left( x + \frac { \pi } { 4 } \right)y=−2cos(x+4π​)

Convert the angle in radians to degrees. - 7π12\frac { 7 \pi } { 12 }127π​

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - 353∘353 ^ { \circ }353∘

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Draw the angle. - $330 ^ { \circ }$

Solve the problem. -An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of $\frac { 1 } { 3 }$ radian is swept out, what is the linear speed of the object?

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 60 ^ { \circ } \right)$

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. - $\sec ^ { 2 } 40 ^ { \circ } - \tan ^ { 2 } 40 ^ { \circ }$

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $64.64 ^ { \circ }$

Solve the problem. -If $\sin \theta = \frac { 1 } { 9 }$ , find $\csc \theta$

Choose the one alternative that best completes the statement or answers the question. -If $\sin \theta = 0.3$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

Find the exact value. Do not use a calculator. - $\cot \frac { \pi } { 6 }$

Find the exact value. Do not use a calculator. - $\cos \frac { 20 \pi } { 3 }$

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

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=5 \sin x+1$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=5 \sin x+1$

Solve the problem. -A gear with a radius of 16 centimeters is turning at $\frac { \pi } { 11 }$ radians/sec. What is the linear speed at a point on the outer edge of the gear?

Solve the problem. -If $\sin \theta = 0.7$ , find the value of $\sin \theta + \sin ( \theta + 2 \pi ) + \sin ( \theta + 4 \pi )$ .

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $5 \pi$ Phase Shift: $- \frac { \pi } { 5 }$

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

Convert the angle in radians to degrees. - $\frac { 7 \pi } { 12 }$

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $353 ^ { \circ }$