Question 1

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta > 0$

Accepted Answer

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

Question 2

Use a calculator to graph the function.
-$y=\sin 2 x+2 x$

Accepted Answer

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

Question 3

On the given graph of $y = \csc x$, sketch the graph of $y = \csc ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Accepted Answer

The answer of  
On the given graph of \(y...

Question 4

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$\begin{array}{l}
b=37 \
B=33^{\circ} 46^{\prime}
\end{array}$

Accepted Answer

A)  $\mathrm { A } = 56 ^ { \circ } 14 ^ { \prime } , \mathrm { c } = 66.6 , \mathrm { a } = 44.5$ 
B)  $\mathrm { A } = 56 ^ { \circ } 14 , \mathrm { c } = 66.6 , \mathrm { a } = 55.3$ 
C)  $\mathrm { A } = 56 ^ { \circ } 144 ^ { \prime } , \mathrm { c } = 67.1 , \mathrm { a } = 44.4$ 
D)  $\mathrm { A } = 56 ^ { \circ } 14 , \mathrm { c } = 44.5 , \mathrm { a } = 66.6$ 
A)  $\mathrm { A } = 56 ^ { \circ } 14 ^ { \prime } , \mathrm { c } = 66.6 , \mathrm { a } = 44.5$ 
B)  $\mathrm { A } = 56 ^ { \circ } 14 , \mathrm { c } = 66.6 , \mathrm { a } = 55.3$ 
C)  $\mathrm { A } = 56 ^ { \circ } 144 ^ { \prime } , \mathrm { c } = 67.1 , \mathrm { a } = 44.4$ 
D)  $\mathrm { A } = 56 ^ { \circ } 14 , \mathrm { c } = 44.5 , \mathrm { a } = 66.6$

Question 5

Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = 4 \sin 2 x + 7 \cos 3 x$$

Accepted Answer

A)  $6 \pi$ 
B)  $2 \pi$ 
C)  Not periodic 
D)  $\pi$ 
A)  $6 \pi$ 
B)  $2 \pi$ 
C)  Not periodic 
D)  $\pi$

Question 6

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

Accepted Answer

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

Question 7

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$60 ^ { \circ } 29 ^ { \prime }$

Accepted Answer

A)  $1.0523$ 
B)  $1.0472$ 
C)  $1.0556$ 
D)  $0.3333$ 
A)  $1.0523$ 
B)  $1.0472$ 
C)  $1.0556$ 
D)  $0.3333$

Question 8

Find the exact solution to the equation without a calculator.
-$\cos ^ { - 1 } ( \cos x ) = 1.8$

Accepted Answer

A)  $0.9$ 
B)  $3.6$ 
C)  $1.8$ 
D)  0 
A)  $0.9$ 
B)  $3.6$ 
C)  $1.8$ 
D)  0

Question 9

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
-y = -cot x

Accepted Answer

A)  Vertical translation up 1 unit 
B)  Reflection across the x-axis and the y-axis 
C)  Vertical translation down 1 unit 
D)  Reflection across the x-axis 
A)  Vertical translation up 1 unit 
B)  Reflection across the x-axis and the y-axis 
C)  Vertical translation down 1 unit 
D)  Reflection across the x-axis

Question 10

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$- 45 ^ { \circ }$

Accepted Answer

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

Question 11

Give the exact value.
-$\cos \frac { \pi } { 3 }$

Accepted Answer

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

Question 12

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$\tan ^ { - 1 } ( 0.5774 )$

Accepted Answer

A)  $60 ^ { \circ }$ 
B)  $32 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
A)  $60 ^ { \circ }$ 
B)  $32 ^ { \circ }$ 
C)  $27 ^ { \circ }$ 
D)  $30 ^ { \circ }$

Question 13

Determine whether the graph of f(x) is a sinusoid.
-$$f ( x ) = 15 \sin x + 7 \cos x$$

Accepted Answer

A) True 
 B)False

Question 14

Find the exact value of the real number y.
-$$y = \arcsin \left( - \frac { 1 } { 2 } \right)$$

Accepted Answer

A)  $\pi$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  $- \frac { \pi } { 6 }$ 
A)  $\pi$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  $- \frac { \pi } { 6 }$

Question 15

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( 8 , - 7 )$; find $\tan \theta$

Accepted Answer

A)  $- \frac { 7 } { 8 }$ 
B)  $- \frac { 8 } { 7 }$ 
C)  $- \frac { 7 } { 11 }$ 
D)  $\frac { 8 } { 11 }$ 
A)  $- \frac { 7 } { 8 }$ 
B)  $- \frac { 8 } { 7 }$ 
C)  $- \frac { 7 } { 11 }$ 
D)  $\frac { 8 } { 11 }$

Question 16

Solve the problem.
-The minimum length $L$ of a highway sag curve can be computed by
$$\mathrm { L } = \frac { \left( \theta _ { 2 } - \theta _ { 1 } \right) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } \tan \alpha ) ^ { \prime } }$$
where $\theta _ { 1 }$ is the downhill grade in degrees $\left( \theta _ { 1 }  0 ^ { \circ } \right) , S$ is the safe stopping distance for a given speed limit, $h$ is the height of the headlights, and $\alpha$ is the alignment of the headlights in degrees. Compute $L$ for a 55-mph speed limit, where $h = 1.7 \mathrm { ft } , \alpha = 0.9 ^ { \circ } , \theta _ { 1 } = - 5 ^ { \circ } , \theta _ { 2 } = 4 ^ { \circ }$, and $\mathrm { S } = 336 \mathrm { ft }$. Round your answer to the nearest foot.

Accepted Answer

A)  $728 \mathrm { ft }$ 
B)  $769 \mathrm { ft }$ 
C)  $748 \mathrm { ft }$ 
D)  $709 \mathrm { ft }$ 
A)  $728 \mathrm { ft }$ 
B)  $769 \mathrm { ft }$ 
C)  $748 \mathrm { ft }$ 
D)  $709 \mathrm { ft }$

Question 17

Graph the function.
-$y=3 \cos 2 x-3 \cos 3 x$

Accepted Answer

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

Question 18

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric
graph.
-$$f ( x ) = \sin ^ { - 1 } 7 x$$

Accepted Answer

A)  Horizontal shrink by a factor of $\frac { 1 } { 7 }$ 
B)  Horizontal stretch by a factor of 7 
C)  Vertical translation up 7 units 
D)  Vertical stretch by a factor of 7 
A)  Horizontal shrink by a factor of $\frac { 1 } { 7 }$ 
B)  Horizontal stretch by a factor of 7 
C)  Vertical translation up 7 units 
D)  Vertical stretch by a factor of 7

Question 19

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$13.38 ^ { \circ }$

Accepted Answer

A)  $13 ^ { \circ } 22 ^ { \prime } 36 ^ { \prime \prime }$ 
B)  $13 ^ { \circ } 22 ^ { \prime } 38 ^ { \prime \prime }$ 
C)  $13 ^ { \circ } 22 ^ { \prime } 54 ^ { \prime \prime }$ 
D)  $13 ^ { \circ } 22 ^ { \prime } 48 ^ { \prime \prime }$ 
A)  $13 ^ { \circ } 22 ^ { \prime } 36 ^ { \prime \prime }$ 
B)  $13 ^ { \circ } 22 ^ { \prime } 38 ^ { \prime \prime }$ 
C)  $13 ^ { \circ } 22 ^ { \prime } 54 ^ { \prime \prime }$ 
D)  $13 ^ { \circ } 22 ^ { \prime } 48 ^ { \prime \prime }$

Question 20

Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = x ^ { 2 } \cos 2 x$$

Accepted Answer

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

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta > 0$

Use a calculator to graph the function. - $y=\sin 2 x+2 x$ $Use a calculator to graph the function. - y=\sin 2 x+2 x$

$On the given graph of y = \csc x , sketch the graph of y = \csc ^ { - 1 } x as defined in the text. Give the domain and the range.$ On the given graph of $y = \csc x$ , sketch the graph of $y = \csc ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - \begin{array}{l} b=37 \\ B=33^{\circ} 46^{\prime} \end{array}$ b=37 B=34

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 4 \sin 2 x + 7 \cos 3 x$

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

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $60 ^ { \circ } 29 ^ { \prime }$

Find the exact solution to the equation without a calculator. - $\cos ^ { - 1 } ( \cos x ) = 1.8$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = -cot x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $- 45 ^ { \circ }$

Give the exact value. - $\cos \frac { \pi } { 3 }$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\tan ^ { - 1 } ( 0.5774 )$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 15 \sin x + 7 \cos x$

Find the exact value of the real number y. - $y = \arcsin \left( - \frac { 1 } { 2 } \right)$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 8 , - 7 )$ ; find $\tan \theta$

Graph the function. - $y=3 \cos 2 x-3 \cos 3 x$ $Graph the function. - y=3 \cos 2 x-3 \cos 3 x$

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - $f ( x ) = \sin ^ { - 1 } 7 x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $13.38 ^ { \circ }$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = x ^ { 2 } \cos 2 x$

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

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - sin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }sinθ=23​​ and tan⁡θ>0\tan \theta > 0tanθ>0

Use a calculator to graph the function. - y=sin⁡2x+2xy=\sin 2 x+2 xy=sin2x+2x

On the given graph of y=csc⁡xy = \csc xy=cscx , sketch the graph of y=csc⁡−1xy = \csc ^ { - 1 } xy=csc−1x as defined in the text. Give the domain and the range.

Solve the right triangle for all missing sides and angles to the nearest tenth. - b=37 B=34

Determine whether the function is periodic. If it is periodic, find the period. - f(x)=4sin⁡2x+7cos⁡3xf ( x ) = 4 \sin 2 x + 7 \cos 3 xf(x)=4sin2x+7cos3x

Graph the function. - y=2sin⁡x+5cos⁡2xy=2 \sin x+5 \cos 2 xy=2sinx+5cos2x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 60∘29′60 ^ { \circ } 29 ^ { \prime }60∘29′

Find the exact solution to the equation without a calculator. - cos⁡−1(cos⁡x)=1.8\cos ^ { - 1 } ( \cos x ) = 1.8cos−1(cosx)=1.8

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = -cot x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - −45∘- 45 ^ { \circ }−45∘

Give the exact value. - cos⁡π3\cos \frac { \pi } { 3 }cos3π​

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - tan⁡−1(0.5774)\tan ^ { - 1 } ( 0.5774 )tan−1(0.5774)

Determine whether the graph of f(x) is a sinusoid. - f(x)=15sin⁡x+7cos⁡xf ( x ) = 15 \sin x + 7 \cos xf(x)=15sinx+7cosx

Find the exact value of the real number y. - y=arcsin⁡(−12)y = \arcsin \left( - \frac { 1 } { 2 } \right)y=arcsin(−21​)

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(8,−7)\mathrm { P } ( 8 , - 7 )P(8,−7) ; find tan⁡θ\tan \thetatanθ

Graph the function. - y=3cos⁡2x−3cos⁡3xy=3 \cos 2 x-3 \cos 3 xy=3cos2x−3cos3x

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - f(x)=sin⁡−17xf ( x ) = \sin ^ { - 1 } 7 xf(x)=sin−17x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 13.38∘13.38 ^ { \circ }13.38∘

Determine whether the function is periodic. If it is periodic, find the period. - f(x)=x2cos⁡2xf ( x ) = x ^ { 2 } \cos 2 xf(x)=x2cos2x

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

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ and $\tan \theta > 0$

Use a calculator to graph the function. - $y=\sin 2 x+2 x$ $Use a calculator to graph the function. - y=\sin 2 x+2 x$

$On the given graph of y = \csc x , sketch the graph of y = \csc ^ { - 1 } x as defined in the text. Give the domain and the range.$ On the given graph of $y = \csc x$ , sketch the graph of $y = \csc ^ { - 1 } x$ as defined in the text. Give the domain and the range.

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - \begin{array}{l} b=37 \\ B=33^{\circ} 46^{\prime} \end{array}$ b=37 B=34

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 4 \sin 2 x + 7 \cos 3 x$

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

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $60 ^ { \circ } 29 ^ { \prime }$

Find the exact solution to the equation without a calculator. - $\cos ^ { - 1 } ( \cos x ) = 1.8$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $- 45 ^ { \circ }$

Give the exact value. - $\cos \frac { \pi } { 3 }$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\tan ^ { - 1 } ( 0.5774 )$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 15 \sin x + 7 \cos x$

Find the exact value of the real number y. - $y = \arcsin \left( - \frac { 1 } { 2 } \right)$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 8 , - 7 )$ ; find $\tan \theta$

Graph the function. - $y=3 \cos 2 x-3 \cos 3 x$ $Graph the function. - y=3 \cos 2 x-3 \cos 3 x$

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - $f ( x ) = \sin ^ { - 1 } 7 x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $13.38 ^ { \circ }$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = x ^ { 2 } \cos 2 x$