Question 1

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

Accepted Answer

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

Question 2

Solve the equation.
-Solve $\cos \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$.

Accepted Answer

A)  $60 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
A)  $60 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $30 ^ { \circ }$

Question 3

Graph the function.
-$$y = 3 \sin \frac { x } { 16 }$$

Accepted Answer

A)  $\frac { \pi } { 16 }$ 
B)  $16 \pi$ 
C)  $32 \pi$ 
D)  3 
A)  $\frac { \pi } { 16 }$ 
B)  $16 \pi$ 
C)  $32 \pi$ 
D)  3

Question 4

Use a calculator to solve for x in the given interval
-$$\sin \theta = - 0.9419 , \pi \leq \theta \leq \frac { 3 \pi } { 2 }$$

Accepted Answer

A)  $4.37$ 
B)  $5.06$ 
C)  $3.48$ 
D)  $- 0.81$ 
A)  $4.37$ 
B)  $5.06$ 
C)  $3.48$ 
D)  $- 0.81$

Question 5

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

Accepted Answer

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

Question 6

Evaluate without using a calculator by using ratios in a reference triangle.
-$$\sin \frac { 5 \pi } { 6 }$$

Accepted Answer

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

Question 7

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

Accepted Answer

A)  $247.5 ^ { \circ }$ 
B)  $270 ^ { \circ }$ 
C)  $202.5 ^ { \circ }$ 
D)  $225 ^ { \circ }$ 
A)  $247.5 ^ { \circ }$ 
B)  $270 ^ { \circ }$ 
C)  $202.5 ^ { \circ }$ 
D)  $225 ^ { \circ }$

Question 8

Determine whether the given function is positive or negative for values of t in the specified quadrant.
-Quadrant III, $\cos t$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 9

Determine the sign (positive or negative) of the given value without use of a calculator.
-$\tan 151 ^ { \circ }$

Accepted Answer

A)  Negative 
B)  Positive 
A)  Negative 
B)  Positive

Question 10

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary.
-$$f ( x ) = \sin 2 \pi x + 2 \cos 2 \pi x$$

Accepted Answer

A)  $\mathrm { a } = 1.78 , \mathrm {~b} = 3.14 , \mathrm {~h} = - 0.18$ 
B)  $\mathrm { a } = 2.23 , \mathrm {~b} = 3.14 , \mathrm {~h} = 0.32$ 
C)  $a = 2.23 , b = 6.28 , h = - 0.18$ 
D)  $a = 3.22 , b = 6.28 , h = 0.32$ 
A)  $\mathrm { a } = 1.78 , \mathrm {~b} = 3.14 , \mathrm {~h} = - 0.18$ 
B)  $\mathrm { a } = 2.23 , \mathrm {~b} = 3.14 , \mathrm {~h} = 0.32$ 
C)  $a = 2.23 , b = 6.28 , h = - 0.18$ 
D)  $a = 3.22 , b = 6.28 , h = 0.32$

Question 11

Evaluate without using a calculator by using ratios in a reference triangle.
-$\sec \frac { 3 \pi } { 4 }$

Accepted Answer

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

Question 12

Solve the problem.
-A pendulum of length $\mathrm { L }$, when displaced horizontally and released, oscillates with harmonic motion according to the equation $y = A \sin ( ( \sqrt { g / L } ) t + \pi / 2 )$, where $y$ is the distance in meters from the rest position $t$ seconds after release, and $g = 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$. Identify the period, amplitude, and phase shift when $\mathrm { A } = 0.10 \mathrm {~m}$ and $\mathrm { L } = 0.98 \mathrm {~m}$.

Accepted Answer

A)  $0.99 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.99 \mathrm {~s}$ 
B)  $1.99 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.50 \mathrm {~s}$ 
C)  $0.63 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.157 \mathrm {~s}$ 
D)  $1.99 \mathrm {~s} , 0.10 \mathrm {~m} , 0.50 \mathrm {~s}$ 
A)  $0.99 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.99 \mathrm {~s}$ 
B)  $1.99 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.50 \mathrm {~s}$ 
C)  $0.63 \mathrm {~s} , 0.10 \mathrm {~m} , - 0.157 \mathrm {~s}$ 
D)  $1.99 \mathrm {~s} , 0.10 \mathrm {~m} , 0.50 \mathrm {~s}$

Question 13

Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = 8 \left| \sin ^ { 3 } x \right|$$

Accepted Answer

A)  Not periodic 
B)  $\pi$ 
C)  $2 \pi$ 
D)  $\frac { \pi } { 2 }$ 
A)  Not periodic 
B)  $\pi$ 
C)  $2 \pi$ 
D)  $\frac { \pi } { 2 }$

Question 14

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$$\mathrm { a } = 19$$
$$\mathrm { A } = 63 ^ { \circ } 37 ^ { \prime }$$

Accepted Answer

A)  $B = 26 ^ { \circ } 23 ^ { \prime } , c = 21.2 , b = 42.8$ 
B)  $B = 26 ^ { \circ } 23 ^ { \prime } , \mathrm { c } = 42.8 , \mathrm {~b} = 21.2$ 
C)  $B = 26 ^ { \circ } 23 ^ { \prime } , \mathrm { c } = 21.3 , \mathrm {~b} = 42.4$ 
D)  $B = 26 ^ { \circ } 23 ^ { \prime } , c = 21.2 , b = 9.4$ 
A)  $B = 26 ^ { \circ } 23 ^ { \prime } , c = 21.2 , b = 42.8$ 
B)  $B = 26 ^ { \circ } 23 ^ { \prime } , \mathrm { c } = 42.8 , \mathrm {~b} = 21.2$ 
C)  $B = 26 ^ { \circ } 23 ^ { \prime } , \mathrm { c } = 21.3 , \mathrm {~b} = 42.4$ 
D)  $B = 26 ^ { \circ } 23 ^ { \prime } , c = 21.2 , b = 9.4$

Question 15

Choose the graph which matches the function.
-$y = 4 \sin 3 x + 2 \sin 2 x$

Accepted Answer

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

Question 16

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = - 2 \cos \frac { \pi x } { 7 } ; g ( x ) = \cos x$$

Accepted Answer

A)  Horizontal stretch by a factor $\frac { 7 } { \pi }$, vertical stretch by a factor of 2 , reflection across $x$-axis 
B)  Horizontal shrink by a factor $\frac { \pi } { 7 }$ vertical shrink by a factor of $\frac { 1 } { 2 }$, reflection across $y$-axis 
C)  Horizontal stretch by a factor $\frac { 7 } { \pi }$, vertical stretch by a factor of 2 , reflection across y-axis 
D)  Horizontal shrink by a factor $\frac { \pi } { 7 }$, vertical stretch by a factor of 2 , reflection across $x$-axis 
A)  Horizontal stretch by a factor $\frac { 7 } { \pi }$, vertical stretch by a factor of 2 , reflection across $x$-axis 
B)  Horizontal shrink by a factor $\frac { \pi } { 7 }$ vertical shrink by a factor of $\frac { 1 } { 2 }$, reflection across $y$-axis 
C)  Horizontal stretch by a factor $\frac { 7 } { \pi }$, vertical stretch by a factor of 2 , reflection across y-axis 
D)  Horizontal shrink by a factor $\frac { \pi } { 7 }$, vertical stretch by a factor of 2 , reflection across $x$-axis

Question 17

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( \sqrt { 17 } , - \sqrt { 6 } ) ;$ find $\sec \theta$

Accepted Answer

A)  $ -\frac{\sqrt{138}}{23} $ 
B)  $ \frac{\sqrt{391}}{23} $ 
C)  $ -\frac{\sqrt{138}}{6} $ 
D)  $ \frac{\sqrt{391}}{17} $ 
A)  $ -\frac{\sqrt{138}}{23} $ 
B)  $ \frac{\sqrt{391}}{23} $ 
C)  $ -\frac{\sqrt{138}}{6} $ 
D)  $ \frac{\sqrt{391}}{17} $

Question 18

Solve the problem.
-Two pulleys, one with a radius of 13 inches and the other with a radius of 8 inches, are connected by a belt. If the larger pulley makes 7 revolutions per minute, how many revolutions per minute does the smaller pulley make? Round your answer to the nearest tenth.

Accepted Answer

A)  $14.9 \mathrm { rpm }$ 
B)  $1.6 \mathrm { rpm }$ 
C)  $0.2 \mathrm { rpm }$ 
D)  $11.4 \mathrm { rpm }$ 
A)  $14.9 \mathrm { rpm }$ 
B)  $1.6 \mathrm { rpm }$ 
C)  $0.2 \mathrm { rpm }$ 
D)  $11.4 \mathrm { rpm }$

Question 19

Evaluate without using a calculator.
-$\csc \theta$, if $\cot \theta = - \frac { 7 } { 10 }$ and $\cos \theta < 0$

Accepted Answer

A)  $\frac { \sqrt { 149 } } { 10 }$ 
B)  $\frac { 7 \sqrt { 149 } } { 149 }$ 
C)  $- \frac { 7 \sqrt { 149 } } { 149 }$ 
D)  $- \frac { \sqrt { 149 } } { 7 }$ 
A)  $\frac { \sqrt { 149 } } { 10 }$ 
B)  $\frac { 7 \sqrt { 149 } } { 149 }$ 
C)  $- \frac { 7 \sqrt { 149 } } { 149 }$ 
D)  $- \frac { \sqrt { 149 } } { 7 }$

Question 20

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

Accepted Answer

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

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

Solve the equation. -Solve $\cos \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$ .

Graph the function. - $y = 3 \sin \frac { x } { 16 }$ $Graph the function. - y = 3 \sin \frac { x } { 16 }$

Use a calculator to solve for x in the given interval - $\sin \theta = - 0.9419 , \pi \leq \theta \leq \frac { 3 \pi } { 2 }$

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

Evaluate without using a calculator by using ratios in a reference triangle. - $\sin \frac { 5 \pi } { 6 }$

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

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, $\cos t$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan 151 ^ { \circ }$

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = \sin 2 \pi x + 2 \cos 2 \pi x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\sec \frac { 3 \pi } { 4 }$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 8 \left| \sin ^ { 3 } x \right|$

Choose the graph which matches the function. - $y = 4 \sin 3 x + 2 \sin 2 x$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = - 2 \cos \frac { \pi x } { 7 } ; g ( x ) = \cos x$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( \sqrt { 17 } , - \sqrt { 6 } ) ;$ find $\sec \theta$

Solve the problem. -Two pulleys, one with a radius of 13 inches and the other with a radius of 8 inches, are connected by a belt. If the larger pulley makes 7 revolutions per minute, how many revolutions per minute does the smaller pulley make? Round your answer to the nearest tenth.

Evaluate without using a calculator. - $\csc \theta$ , if $\cot \theta = - \frac { 7 } { 10 }$ and $\cos \theta < 0$

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

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=sec⁡(x3)y=\sec \left(\frac{x}{3}\right)y=sec(3x​)

Solve the equation. -Solve cos⁡θ=32\cos \theta = \frac { \sqrt { 3 } } { 2 }cosθ=23​​ for θ\thetaθ , where 0∘≤θ≤90∘0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }0∘≤θ≤90∘ .

Graph the function. - y=3sin⁡x16y = 3 \sin \frac { x } { 16 }y=3sin16x​

Use a calculator to solve for x in the given interval - sin⁡θ=−0.9419,π≤θ≤3π2\sin \theta = - 0.9419 , \pi \leq \theta \leq \frac { 3 \pi } { 2 }sinθ=−0.9419,π≤θ≤23π​

Graph the function. - y=sin⁡3xy = \sin 3 xy=sin3x

Evaluate without using a calculator by using ratios in a reference triangle. - sin⁡5π6\sin \frac { 5 \pi } { 6 }sin65π​