Question 1

Graph the function.
-$y=\frac{3}{4} \sin \frac{2}{3} x$

Accepted Answer

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

Question 2

Solve.
-The angle of reflection $\theta$ of a ray from air to a medium of index $n$ is given by Snell's Law to be $\sin \theta = 1 / n$. Find $\theta$ if $n = 9 / 8$.

Accepted Answer

A)  $1.6 ^ { \circ }$ 
B)  $62.7 ^ { \circ }$ 
C)  $117.3 ^ { \circ }$ 
D)  $27.3 ^ { \circ }$ 
A)  $1.6 ^ { \circ }$ 
B)  $62.7 ^ { \circ }$ 
C)  $117.3 ^ { \circ }$ 
D)  $27.3 ^ { \circ }$

Question 3

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$\sin ^ { - 1 } ( 0.533 )$

Accepted Answer

A)  $64.42 ^ { \circ }$ 
B)  $32.21 ^ { \circ }$ 
C)  $57.79 ^ { \circ }$ 
D)  $28.06 ^ { \circ }$ 
A)  $64.42 ^ { \circ }$ 
B)  $32.21 ^ { \circ }$ 
C)  $57.79 ^ { \circ }$ 
D)  $28.06 ^ { \circ }$

Question 4

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\sec 0.1296$

Accepted Answer

A)  $1.0085$ 
B)  $0.9916$ 
C)  $0.1292$ 
D)  $0.1303$ 
A)  $1.0085$ 
B)  $0.9916$ 
C)  $0.1292$ 
D)  $0.1303$

Question 5

Find the angle in degrees that describes the compass bearing.
-NW

Accepted Answer

A)  $315 ^ { \circ }$ 
B)  $270 ^ { \circ }$ 
C)  $292.5 ^ { \circ }$ 
D)  $337.5 ^ { \circ }$ 
A)  $315 ^ { \circ }$ 
B)  $270 ^ { \circ }$ 
C)  $292.5 ^ { \circ }$ 
D)  $337.5 ^ { \circ }$

Question 6

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = - 6 \cos 3 x ; g ( x ) = \cos x$$

Accepted Answer

A)  Horizontal shrink by a factor $\frac { 1 } { 6 }$, vertical stretch by a factor of 3 , reflection across $y$-axis 
B)  Horizontal stretch by a factor 3 , vertical stretch by a factor of 6 , reflection across $x$-axis 
C)  Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $\mathrm { y }$-axis 
D)  Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $x$-axis 
A)  Horizontal shrink by a factor $\frac { 1 } { 6 }$, vertical stretch by a factor of 3 , reflection across $y$-axis 
B)  Horizontal stretch by a factor 3 , vertical stretch by a factor of 6 , reflection across $x$-axis 
C)  Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $\mathrm { y }$-axis 
D)  Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $x$-axis

Question 7

Solve for x in the given interval.
-$\tan x = - \frac { \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pi$

Accepted Answer

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

Question 8

Find the amplitude of the function.
-$$y = 5 \cos \frac { 1 } { 4 } x$$

Accepted Answer

A)  $\frac { \pi } { 5 }$ 
B)  5 
C)  $8 \pi$ 
D)  $\frac { 5 \pi } { 4 }$ 
A)  $\frac { \pi } { 5 }$ 
B)  5 
C)  $8 \pi$ 
D)  $\frac { 5 \pi } { 4 }$

Question 9

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\sin \left( \frac { \pi } { 12 } \right)$

Accepted Answer

A)  $0.6503$ 
B)  $0.9659$ 
C)  $0.0046$ 
D)  $0.2588$ 
A)  $0.6503$ 
B)  $0.9659$ 
C)  $0.0046$ 
D)  $0.2588$

Question 10

Solve the right triangle for all missing sides and angles to the nearest tenth.
-

Accepted Answer

A)  $27.04$ 
B)  $37.21$ 
C)  $63.31$ 
D)  $33.42$ 
A)  $27.04$ 
B)  $37.21$ 
C)  $63.31$ 
D)  $33.42$

Question 11

Find an algebraic expression equivalent to the given expression.
-$\tan \left( \arccos \frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 5 } } \right)$

Accepted Answer

A)  $\frac { \sqrt { u ^ { 2 } + 5 } } { 5 }$ 
B)  $\frac { \sqrt { 5 u ^ { 2 } + 25 } } { 5 }$ 
C)  $\frac { u \sqrt { u ^ { 2 } + 5 } } { u 2 + 5 }$ 
D)  $\frac { \sqrt { 5 } } { u }$ 
A)  $\frac { \sqrt { u ^ { 2 } + 5 } } { 5 }$ 
B)  $\frac { \sqrt { 5 u ^ { 2 } + 25 } } { 5 }$ 
C)  $\frac { u \sqrt { u ^ { 2 } + 5 } } { u 2 + 5 }$ 
D)  $\frac { \sqrt { 5 } } { u }$

Question 12

Graph the function.
-$y=\cot 4 x$

Accepted Answer

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

Question 13

Solve the problem.
-The transverse (vertical) displacement of a traveling wave on a stretched string is represented by the equation $y = A \cos \frac { 2 \pi } { \lambda } ( x - V t )$. Find the period, amplitude, and phase shift of this function, given that $A = 5 , \lambda = 5$ in, $\mathrm { V } = \frac { 1 } { 2 } \mathrm { in } / \mathrm { sec }$, and $\mathrm { t } = 2 \mathrm { sec } .$

Accepted Answer

A)  $\pi , 5 , - 1$ 
B)  $5,5,1$ 
C)  $0.20,5,0.20$ 
D)  $5,5 , - 1$ 
A)  $\pi , 5 , - 1$ 
B)  $5,5,1$ 
C)  $0.20,5,0.20$ 
D)  $5,5 , - 1$

Question 14

Find the specified quantity.
-Find the period of $y = 3 \sin \left( 4 x + \frac { \pi } { 2 } \right)$.

Accepted Answer

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

Question 15

Graph the function.
-$y=5 \sin 3 x+5 \sin 2 x$

Accepted Answer

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

Question 16

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.
-Amplitude $\frac { 1 } { 4 }$, period $5 \pi$, point $( 0,0 )$

Accepted Answer

A)  $y = \frac { 1 } { 4 } \sin \frac { 5 x } { 2 }$ 
B)  $y = \frac { 1 } { 4 } \sin \frac { 2 \pi x } { 5 }$ 
C)  $y = \frac { 1 } { 4 } \sin 5 \pi x$ 
D)  $y = \frac { 1 } { 4 } \sin \frac { 2 x } { 5 }$ 
A)  $y = \frac { 1 } { 4 } \sin \frac { 5 x } { 2 }$ 
B)  $y = \frac { 1 } { 4 } \sin \frac { 2 \pi x } { 5 }$ 
C)  $y = \frac { 1 } { 4 } \sin 5 \pi x$ 
D)  $y = \frac { 1 } { 4 } \sin \frac { 2 x } { 5 }$

Question 17

Evaluate without using a calculator by using ratios in a reference triangle.
-$\sec 240 ^ { \circ }$

Accepted Answer

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

Question 18

Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 3 \cos 20 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Accepted Answer

A)  The maximum height of 6 inches is first reached after 5 seconds. 
B)  The maximum height of 6 inches is first reached after 10 seconds. 
C)  The maximum height of 3 inches is first reached after 10 seconds. 
D)  The maximum height of 3 inches is first reached after $0.05$ seconds. 
A)  The maximum height of 6 inches is first reached after 5 seconds. 
B)  The maximum height of 6 inches is first reached after 10 seconds. 
C)  The maximum height of 3 inches is first reached after 10 seconds. 
D)  The maximum height of 3 inches is first reached after $0.05$ seconds.

Question 19

Solve.
-The equation $\theta = \cos ^ { - 1 } ( \mathrm { R } / \mathrm { Z } )$ gives the phase angle between $R$ and $Z$ in an $\mathrm { AC }$ circuit. Find $\theta$ if $R = 50$ ohms and $Z = 100$ ohms.

Accepted Answer

A)  $30.0 ^ { \circ }$ 
B)  $60.0 ^ { \circ }$ 
C)  $120.0 ^ { \circ }$ 
D)  $0.7 ^ { \circ }$ 
A)  $30.0 ^ { \circ }$ 
B)  $60.0 ^ { \circ }$ 
C)  $120.0 ^ { \circ }$ 
D)  $0.7 ^ { \circ }$

Question 20

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$292.41 ^ { \circ }$

Accepted Answer

A)  $292 ^ { \circ } 25 ^ { \prime } 35 ^ { \prime \prime }$ 
B)  $292 ^ { \circ } 24 ^ { \prime } 41 ^ { \prime \prime }$ 
C)  $292 ^ { \circ } 24 ^ { \prime } 36 ^ { \prime \prime }$ 
D)  $292 ^ { \circ } 35 ^ { \prime } 41 ^ { \prime \prime }$ 
A)  $292 ^ { \circ } 25 ^ { \prime } 35 ^ { \prime \prime }$ 
B)  $292 ^ { \circ } 24 ^ { \prime } 41 ^ { \prime \prime }$ 
C)  $292 ^ { \circ } 24 ^ { \prime } 36 ^ { \prime \prime }$ 
D)  $292 ^ { \circ } 35 ^ { \prime } 41 ^ { \prime \prime }$

Graph the function. - $y=\frac{3}{4} \sin \frac{2}{3} x$ $Graph the function. - y=\frac{3}{4} \sin \frac{2}{3} x$

Solve. -The angle of reflection $\theta$ of a ray from air to a medium of index $n$ is given by Snell's Law to be $\sin \theta = 1 / n$ . Find $\theta$ if $n = 9 / 8$ .

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\sin ^ { - 1 } ( 0.533 )$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\sec 0.1296$

Find the angle in degrees that describes the compass bearing. -NW

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = - 6 \cos 3 x ; g ( x ) = \cos x$

Solve for x in the given interval. - $\tan x = - \frac { \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pi$

Find the amplitude of the function. - $y = 5 \cos \frac { 1 } { 4 } x$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\sin \left( \frac { \pi } { 12 } \right)$

Solve the right triangle for all missing sides and angles to the nearest tenth. -

Find an algebraic expression equivalent to the given expression. - $\tan \left( \arccos \frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 5 } } \right)$

Graph the function. - $y=\cot 4 x$ $Graph the function. - y=\cot 4 x$

Find the specified quantity. -Find the period of $y = 3 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

Graph the function. - $y=5 \sin 3 x+5 \sin 2 x$ $Graph the function. - y=5 \sin 3 x+5 \sin 2 x$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude $\frac { 1 } { 4 }$ , period $5 \pi$ , point $( 0,0 )$

Evaluate without using a calculator by using ratios in a reference triangle. - $\sec 240 ^ { \circ }$

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 3 \cos 20 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Solve. -The equation $\theta = \cos ^ { - 1 } ( \mathrm { R } / \mathrm { Z } )$ gives the phase angle between $R$ and $Z$ in an $\mathrm { AC }$ circuit. Find $\theta$ if $R = 50$ ohms and $Z = 100$ ohms.

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $292.41 ^ { \circ }$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 4: Trigonometric Functions

Graph the function. - y=34sin⁡23xy=\frac{3}{4} \sin \frac{2}{3} xy=43​sin32​x

Solve. -The angle of reflection θ\thetaθ of a ray from air to a medium of index nnn is given by Snell's Law to be sin⁡θ=1/n\sin \theta = 1 / nsinθ=1/n . Find θ\thetaθ if n=9/8n = 9 / 8n=9/8 .

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - sin⁡−1(0.533)\sin ^ { - 1 } ( 0.533 )sin−1(0.533)

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - sec⁡0.1296\sec 0.1296sec0.1296

Find the angle in degrees that describes the compass bearing. -NW

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - f(x)=−6cos⁡3x;g(x)=cos⁡xf ( x ) = - 6 \cos 3 x ; g ( x ) = \cos xf(x)=−6cos3x;g(x)=cosx

Solve for x in the given interval. - tan⁡x=−33,π2≤x≤π\tan x = - \frac { \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pitanx=−33​​,2π​≤x≤π

Find the amplitude of the function. - y=5cos⁡14xy = 5 \cos \frac { 1 } { 4 } xy=5cos41​x

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - sin⁡(π12)\sin \left( \frac { \pi } { 12 } \right)sin(12π​)

Solve the right triangle for all missing sides and angles to the nearest tenth. -

Find an algebraic expression equivalent to the given expression. - tan⁡(arccos⁡uu2+5)\tan \left( \arccos \frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 5 } } \right)tan(arccosu2+5​u​)

Graph the function. - y=cot⁡4xy=\cot 4 xy=cot4x

Find the specified quantity. -Find the period of y=3sin⁡(4x+π2)y = 3 \sin \left( 4 x + \frac { \pi } { 2 } \right)y=3sin(4x+2π​) .

Graph the function. - y=5sin⁡3x+5sin⁡2xy=5 \sin 3 x+5 \sin 2 xy=5sin3x+5sin2x

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 14\frac { 1 } { 4 }41​ , period 5π5 \pi5π , point (0,0)( 0,0 )(0,0)

Evaluate without using a calculator by using ratios in a reference triangle. - sec⁡240∘\sec 240 ^ { \circ }sec240∘

Solve the problem. -The position of a weight attached to a spring is s(t)=−3cos⁡20πts ( t ) = - 3 \cos 20 \pi ts(t)=−3cos20πt inches after ttt seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Solve. -The equation θ=cos⁡−1(R/Z)\theta = \cos ^ { - 1 } ( \mathrm { R } / \mathrm { Z } )θ=cos−1(R/Z) gives the phase angle between RRR and ZZZ in an AC\mathrm { AC }AC circuit. Find θ\thetaθ if R=50R = 50R=50 ohms and Z=100Z = 100Z=100 ohms.

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 292.41∘292.41 ^ { \circ }292.41∘

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Graph the function. - $y=\frac{3}{4} \sin \frac{2}{3} x$ $Graph the function. - y=\frac{3}{4} \sin \frac{2}{3} x$

Solve. -The angle of reflection $\theta$ of a ray from air to a medium of index $n$ is given by Snell's Law to be $\sin \theta = 1 / n$ . Find $\theta$ if $n = 9 / 8$ .

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\sin ^ { - 1 } ( 0.533 )$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\sec 0.1296$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = - 6 \cos 3 x ; g ( x ) = \cos x$

Solve for x in the given interval. - $\tan x = - \frac { \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pi$

Find the amplitude of the function. - $y = 5 \cos \frac { 1 } { 4 } x$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\sin \left( \frac { \pi } { 12 } \right)$

Find an algebraic expression equivalent to the given expression. - $\tan \left( \arccos \frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 5 } } \right)$

Graph the function. - $y=\cot 4 x$ $Graph the function. - y=\cot 4 x$

Find the specified quantity. -Find the period of $y = 3 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

Graph the function. - $y=5 \sin 3 x+5 \sin 2 x$ $Graph the function. - y=5 \sin 3 x+5 \sin 2 x$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude $\frac { 1 } { 4 }$ , period $5 \pi$ , point $( 0,0 )$

Evaluate without using a calculator by using ratios in a reference triangle. - $\sec 240 ^ { \circ }$

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 3 \cos 20 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Solve. -The equation $\theta = \cos ^ { - 1 } ( \mathrm { R } / \mathrm { Z } )$ gives the phase angle between $R$ and $Z$ in an $\mathrm { AC }$ circuit. Find $\theta$ if $R = 50$ ohms and $Z = 100$ ohms.

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $292.41 ^ { \circ }$