Question 1

Convert the angle in radians to degrees.
-$$\frac { 12 \pi } { 3 }$$

Accepted Answer

A)  $720 ^ { \circ }$ 
B)  $719 ^ { \circ }$ 
C)  $722 ^ { \circ }$ 
D)  $721 ^ { \circ }$ 
A)  $720 ^ { \circ }$ 
B)  $719 ^ { \circ }$ 
C)  $722 ^ { \circ }$ 
D)  $721 ^ { \circ }$

Question 2

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 3

Find the phase shift of the function.
-$$y = 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 2 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $\pi$ units to the left 
A)  $\frac { \pi } { 2 }$ units to the left 
B)  $3 \pi$ units to the right 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $\pi$ units to the left

Question 4

Draw the angle.
-$- 150 ^ { \circ }$

Accepted Answer

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

Question 5

Solve the problem.
-The data below represent the average monthly cost of natural gas in an Oregon home. $$\begin{array}{l}
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \
\hline \text { Cost } & 21.20 & 28.24 & 44.73 & 67.25 & 89.77 & 106.26
\end{array}\\
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \
\hline \text { Cost } & 111.30 & 106.26 & 89.77 & 67.25 & 43.73 & 28.24
\end{array}
\end{array}$$

Above is the graph of $45.05 \sin x$ superimposed over a scatter diagram of the data. Find the sinusoidal function o form $y = A \sin ( \omega x - \varphi ) + B$ which best fits the data.

Accepted Answer

A)  $y = 45.05 \sin \left( \frac { \pi } { 8 } t + 12 \right) + 21.20$ 
B)  $y = 45.05 \sin \left( \frac { \pi } { 4 } x - \frac { 2 \pi } { 3 } \right) + 21.20$ 
C)  $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 66.25$ 
D)  $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 12 } \right) + 66.25$ 
A)  $y = 45.05 \sin \left( \frac { \pi } { 8 } t + 12 \right) + 21.20$ 
B)  $y = 45.05 \sin \left( \frac { \pi } { 4 } x - \frac { 2 \pi } { 3 } \right) + 21.20$ 
C)  $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 66.25$ 
D)  $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 12 } \right) + 66.25$

Question 6

Graph the function.
-$$y = 3 \sec \left( \frac { 1 } { 4 } x \right)$$

A)

Accepted Answer

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

Question 7

Solve the problem.
-A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour
Rounded to the nearest whole number.

Accepted Answer

A)  9 mph 
B)  47 mph 
C)  28 mph 
D)  56 mph 
A)  9 mph 
B)  47 mph 
C)  28 mph 
D)  56 mph

Question 8

Solve the problem.
-An irrigation sprinkler in a field of lettuce sprays water over a distance of 35 feet as it rotates through an angle of 135°. What area of the field receives water? If necessary, round the answer to two decimal places. A) $459.38 \mathrm { ft } ^ { 2 }$

Accepted Answer

B)  $2,886.34 \mathrm { ft } ^ { 2 }$ 
C)  $1,443.17 \mathrm { ft } ^ { 2 }$ 
D)  $41.23 \mathrm { ft } ^ { 2 }$ 
B)  $2,886.34 \mathrm { ft } ^ { 2 }$ 
C)  $1,443.17 \mathrm { ft } ^ { 2 }$ 
D)  $41.23 \mathrm { ft } ^ { 2 }$

Question 9

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

Accepted Answer

A)  $y = 5 \sin ( x - 3 )$ 
B)  $y = \sin ( 5 x + 3 )$ 
C)  $y = 5 \sin ( 2 x + 6 )$ 
D)  $y = 5 \sin \left( \frac { 1 } { 2 } x - 6 \right)$ 
A)  $y = 5 \sin ( x - 3 )$ 
B)  $y = \sin ( 5 x + 3 )$ 
C)  $y = 5 \sin ( 2 x + 6 )$ 
D)  $y = 5 \sin \left( \frac { 1 } { 2 } x - 6 \right)$

Question 10

Without graphing the function, determine its amplitude or period as requested.
-$y = \cos 3 x \quad$ Find the period.

Accepted Answer

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

Question 11

Find an equation for the graph.
-

Accepted Answer

A)  $y = 4 \cos ( 2 x )$ 
B)  $y = - 4 \cos ( 2 x )$ 
C)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
D)  $y = 4 \sin ( 2 x )$ 
A)  $y = 4 \cos ( 2 x )$ 
B)  $y = - 4 \cos ( 2 x )$ 
C)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
D)  $y = 4 \sin ( 2 x )$

Question 12

Solve the problem.
-If friction is ignored, the time t (in seconds) required for a block to slide down an inclined plane is given by the formula $$t = \sqrt { \frac { 2 a } { g \sin \theta \cos \theta } }$$
where $a$ is the length (in feet) of the base and $g \approx 32$ feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base $a = 14$ when $\theta = 45 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a second.

Accepted Answer

A)  $1.3 \mathrm { sec }$ 
B)  $0.3 \mathrm { sec }$ 
C)  $1.4 \mathrm { sec }$ 
D)  $1.1 \mathrm { sec }$ 
A)  $1.3 \mathrm { sec }$ 
B)  $0.3 \mathrm { sec }$ 
C)  $1.4 \mathrm { sec }$ 
D)  $1.1 \mathrm { sec }$

Question 13

Find the exact value. Do not use a calculator.
-$\cos ( - \pi )$

Accepted Answer

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

Question 14

Convert the angle to a decimal in degrees. Round the answer to two decimal places.
-$$59 ^ { \circ } 6 ^ { \prime } 24 ^ { \prime \prime }$$

Accepted Answer

A)  59.11° 
B)  59.12° 
C)  59.17° 
D)  59.07° 
A)  59.11° 
B)  59.12° 
C)  59.17° 
D)  59.07°

Question 15

Solve the problem.
-A town's average monthly temperature data is represented in the table below: $$\begin{array} { l | c } 
{ \text { Month, x } } & \begin{array} { c } 
\text { Average Monthl } \
\text { Temperature, }
\end{array} \
\hline \text { January, } 1 & 27.9 \
\text { February, 2 } & 30.1 \
\text { March, } 3 & 39.8 \
\text { April, } 4 & 55.8 \
\text { May, 5 } & 70.4 \
\text { June, } 6 & 79.9 \
\text { July, } 7 & 82.6 \
\text { August, } 8 & 77.9 \
\text { September, } 9 & 77.9 \
\text { October, } 10 & 56.3 \
\text { November, } 11 & 43.4 \
\text { December, } 12 & 31.1
\end{array}$$ Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ that fits the data.

Accepted Answer

A)  $y = 82.6 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 27.9$ 
B)  $y = 27.9 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 82.6$ 
C)  $y = 55.25 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 27.35$ 
D)  $y = 27.35 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 55.25$ 
A)  $y = 82.6 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 27.9$ 
B)  $y = 27.9 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 82.6$ 
C)  $y = 55.25 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 27.35$ 
D)  $y = 27.35 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 55.25$

Question 16

Answer the question.
-Which one of the equations below matches the graph?

Accepted Answer

A)  $y = 4 \sin \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = 2 \cos \left( \frac { 1 } { 4 } x \right)$ 
D)  $y = 4 \cos ( 2 x )$ 
A)  $y = 4 \sin \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = 2 \cos \left( \frac { 1 } { 4 } x \right)$ 
D)  $y = 4 \cos ( 2 x )$

Question 17

Graph the function.
-$y=-\tan (x+\pi)$
 
 A)

Accepted Answer

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

Question 18

Solve the problem.
-The following data represents the average percent of possible sunshine for a certain city in Indiana. $\begin{array}{l|c}
\text { Month, x } & \begin{array}{c}
\text { Average Percent of } \
\text { Possible Sunshine }
\end{array} \
\hline \text { January, 1 } & 46 \
\text { February, 2 } & 51 \
\text { March, 3 } & 55 \
\text { April, 4 } & 60 \
\text { May, 5 } & 68 \
\text { June, 6 } & 73 \
\text { July, 7 } & 75 \
\text { August, 8 } & 74 \
\text { September, 9 } & 68 \
\text { October, 10 } & 62 \
\text { November, 11 } & 41 \
\text { December, 12 } & 38
\end{array}$
Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 19

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?

Accepted Answer

A)  $17.79 \mathrm { in } ^ { 2 }$ 
B)  $35.59 \mathrm { in } ^ { 2 }$ 
C)  $302.49 \mathrm { in } ^ { 2 }$ 
D)  $604.97 \mathrm { in } ^ { 2 }$ 
A)  $17.79 \mathrm { in } ^ { 2 }$ 
B)  $35.59 \mathrm { in } ^ { 2 }$ 
C)  $302.49 \mathrm { in } ^ { 2 }$ 
D)  $604.97 \mathrm { in } ^ { 2 }$

Question 20

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

Accepted Answer

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

Convert the angle in radians to degrees. - $\frac { 12 \pi } { 3 }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 60 ^ { \circ } \right)$

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$

Draw the angle. - $- 150 ^ { \circ }$

Solve the problem. -A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour Rounded to the nearest whole number.

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

Without graphing the function, determine its amplitude or period as requested. - $y = \cos 3 x \quad$ Find the period.

Find an equation for the graph. -

Find the exact value. Do not use a calculator. - $\cos ( - \pi )$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $59 ^ { \circ } 6 ^ { \prime } 24 ^ { \prime \prime }$

Answer the question. -Which one of the equations below matches the graph?

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?

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

Review

Filters

Exam 5: Trigonometric Functions

Convert the angle in radians to degrees. - 12π3\frac { 12 \pi } { 3 }312π​

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∘)

Find the phase shift of the function. - y=3cos⁡(12x+π2)y = 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)y=3cos(21​x+2π​)

Draw the angle. - −150∘- 150 ^ { \circ }−150∘

Graph the function. - y=3sec⁡(14x)y = 3 \sec \left( \frac { 1 } { 4 } x \right)y=3sec(41​x) A) B) C) D)

Solve the problem. -A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be moving when the wheels are rotating at 430 revolutions per minute? Express the answer in miles per hour Rounded to the nearest whole number.

Write the equation of a sine function that has the given characteristics. -Amplitude: 5 Period: π\piπ Phase Shift: −3- 3−3

Without graphing the function, determine its amplitude or period as requested. - y=cos⁡3xy = \cos 3 x \quady=cos3x Find the period.

Find an equation for the graph. -

Find the exact value. Do not use a calculator. - cos⁡(−π)\cos ( - \pi )cos(−π)

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - 59∘6′24′′59 ^ { \circ } 6 ^ { \prime } 24 ^ { \prime \prime }59∘6′24′′

Answer the question. -Which one of the equations below matches the graph?

Graph the function. - y=−tan⁡(x+π)y=-\tan (x+\pi)y=−tan(x+π) A) B) C) D)

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - r=17\mathrm { r } = 17r=17 inches, θ=120∘,A=\theta = 120 ^ { \circ } , \mathrm { A } =θ=120∘,A= ?

Graph the function. - y=tan⁡(x−π4)\mathrm { y } = \tan \left( \mathrm { x } - \frac { \pi } { 4 } \right)y=tan(x−4π​) A) B) C) D)

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

Review

Filters

Convert the angle in radians to degrees. - $\frac { 12 \pi } { 3 }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\sin \left( - 60 ^ { \circ } \right)$

Find the phase shift of the function. - $y = 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$

Draw the angle. - $- 150 ^ { \circ }$

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

Without graphing the function, determine its amplitude or period as requested. - $y = \cos 3 x \quad$ Find the period.

Find the exact value. Do not use a calculator. - $\cos ( - \pi )$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $59 ^ { \circ } 6 ^ { \prime } 24 ^ { \prime \prime }$

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $\mathrm { r } = 17$ inches, $\theta = 120 ^ { \circ } , \mathrm { A } =$ ?