Question 1

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = \cos \frac { x } { 5 } ; g ( x ) = \cos x$$

Accepted Answer

A)  Horizontal shrink by a factor of $\frac { 1 } { 5 }$ 
B)  Horizontal stretch by a factor of 5 
C)  Vertical stretch by a factor of 5 
D)  Vertical shrink by a factor of $\frac { 1 } { 5 }$ 
A)  Horizontal shrink by a factor of $\frac { 1 } { 5 }$ 
B)  Horizontal stretch by a factor of 5 
C)  Vertical stretch by a factor of 5 
D)  Vertical shrink by a factor of $\frac { 1 } { 5 }$

Question 2

Choose the graph which matches the function.
-$$f ( x ) = \sqrt { 11 } \cos 3.7 x$$

Accepted Answer

A)  No damping 
B)  Damping factor $= 3.7$, damping occurs as $x \rightarrow 0$ 
C)  Damping factor $= \sqrt { 11 }$, damping occurs as $x \rightarrow \infty$ 
D)  Damping factor $= \sqrt { 11 }$, damping occurs as $x \rightarrow 0$ 
A)  No damping 
B)  Damping factor $= 3.7$, damping occurs as $x \rightarrow 0$ 
C)  Damping factor $= \sqrt { 11 }$, damping occurs as $x \rightarrow \infty$ 
D)  Damping factor $= \sqrt { 11 }$, damping occurs as $x \rightarrow 0$

Question 3

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$\arcsin 0.57$

Accepted Answer

A)  $34.75 ^ { \circ }$ 
B)  $29.68 ^ { \circ }$ 
C)  $55.25 ^ { \circ }$ 
D)  $69.5 ^ { \circ }$ 
A)  $34.75 ^ { \circ }$ 
B)  $29.68 ^ { \circ }$ 
C)  $55.25 ^ { \circ }$ 
D)  $69.5 ^ { \circ }$

Question 4

Solve the problem.
-When the angle of elevation of the sun is $\theta$, a tree casts a shadow. Write a formula which expresses the length of the tree's shadow, $y$, as a function of the angle $\theta$ and the height of the tree, $x$.

Accepted Answer

A)  $y = x \cos \theta$ 
B)  $y = x \cot \theta$ 
C)  $y = \frac { \cot \theta } { x }$ 
D)  $y = x \tan \theta$ 
A)  $y = x \cos \theta$ 
B)  $y = x \cot \theta$ 
C)  $y = \frac { \cot \theta } { x }$ 
D)  $y = x \tan \theta$

Question 5

Solve.
-The equation $\theta _ { 2 } = \tan ^ { - 1 } ( \propto \mathrm { C } / \mathrm { G } )$ gives the phase angle of impedance in the parallel portion of a distributed constant circuit. Find $\theta _ { 2 }$ if $\omega = 130$ radians $/ \mathrm { sec } , \mathrm { C } = 0.01 \mu \mathrm { F } / \mathrm { km }$, and $\mathrm { G } = 1.45 \mu$ siemens/ $\mathrm { km }$.

Accepted Answer

A)  $83.6 ^ { \circ }$ 
B)  $40.1 ^ { \circ }$ 
C)  $89.3 ^ { \circ }$ 
D)  $0.7 ^ { \circ }$ 
A)  $83.6 ^ { \circ }$ 
B)  $40.1 ^ { \circ }$ 
C)  $89.3 ^ { \circ }$ 
D)  $0.7 ^ { \circ }$

Question 6

Graph the function.
-$$y = - 3 \cos \frac { 1 } { 2 } x$$

Accepted Answer

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

Question 7

Solve the problem.
-Radio direction finders are set up at points $\mathrm { A }$ and $\mathrm { B } , 7.24 \mathrm { mi }$ apart on an east-west line. From $A$ it is found that the bearing of a signal from a transmitter is $\mathrm { N } \mathrm {} 50.2 ^ { \circ } \mathrm { E }$, while from B it is $\mathrm { N } 39.8 ^ { \circ } \mathrm { W }$. Find the distance of the transmitter from $B$, to the nearest hundredth of a mile.

Accepted Answer

A)  $4.13 \mathrm { mi }$ 
B)  $6.06 \mathrm { mi }$ 
C)  $4.63 \mathrm { mi }$ 
D)  $5.56 \mathrm { mi }$ 
A)  $4.13 \mathrm { mi }$ 
B)  $6.06 \mathrm { mi }$ 
C)  $4.63 \mathrm { mi }$ 
D)  $5.56 \mathrm { mi }$

Question 8

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$$c = 37$$
$$\mathrm { B } = 28 ^ { \circ } 31 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { A } = 61 ^ { \circ } 2 ^ { \prime } , \mathrm { a } = 17.5 , \mathrm {~b} = 32.6$ 
B)  $\mathrm { A } = 61 ^ { \circ } 29 ^ { \prime } , \mathrm { a } = 17.7 , \mathrm {~b} = 20.1$ 
C)  $\mathrm { A } = 61 ^ { \circ } 2 ^ { \circ } , \mathrm { a } = 32.5 , \mathrm {~b} = 17.7$ 
D)  $\mathrm { A } = 61 ^ { \circ } 29 ^ { \prime } , \mathrm { a } = 17.7 , \mathrm {~b} = 32.5$ 
A)  $\mathrm { A } = 61 ^ { \circ } 2 ^ { \prime } , \mathrm { a } = 17.5 , \mathrm {~b} = 32.6$ 
B)  $\mathrm { A } = 61 ^ { \circ } 29 ^ { \prime } , \mathrm { a } = 17.7 , \mathrm {~b} = 20.1$ 
C)  $\mathrm { A } = 61 ^ { \circ } 2 ^ { \circ } , \mathrm { a } = 32.5 , \mathrm {~b} = 17.7$ 
D)  $\mathrm { A } = 61 ^ { \circ } 29 ^ { \prime } , \mathrm { a } = 17.7 , \mathrm {~b} = 32.5$

Question 9

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$$\begin{array} { l } 
\mathrm { c } = 24 \
\mathrm {~B} = 67 ^ { \circ }
\end{array}$$

Accepted Answer

A)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 26.1 , \mathrm {~b} = 61.4$ 
B)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 9.4 , \mathrm {~b} = 22.1$ 
C)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 10.2 , \mathrm {~b} = 26.1$ 
D)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 61.4 , \mathrm {~b} = 26.1$ 
A)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 26.1 , \mathrm {~b} = 61.4$ 
B)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 9.4 , \mathrm {~b} = 22.1$ 
C)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 10.2 , \mathrm {~b} = 26.1$ 
D)  $\mathrm { A } = 23 ^ { \circ } , \mathrm { a } = 61.4 , \mathrm {~b} = 26.1$

Question 10

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$$\mathrm { C } = 14$$
$$B = 40 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 10.7$ 
B)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 11.7 , \mathrm {~b} = 9$ 
C)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 10.7 , \mathrm {~b} = 11.7$ 
D)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 10.7 , \mathrm {~b} = 9$ 
A)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 10.7$ 
B)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 11.7 , \mathrm {~b} = 9$ 
C)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 10.7 , \mathrm {~b} = 11.7$ 
D)  $\mathrm { A } = 50 ^ { \circ } , \mathrm { a } = 10.7 , \mathrm {~b} = 9$

Question 11

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

Accepted Answer

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

Question 12

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
-4

Accepted Answer

A)  $458.36 ^ { \circ }$ 
B)  $229.48 ^ { \circ }$ 
C)  $458.06 ^ { \circ }$ 
D)  $229.18 ^ { \circ }$ 
A)  $458.36 ^ { \circ }$ 
B)  $229.48 ^ { \circ }$ 
C)  $458.06 ^ { \circ }$ 
D)  $229.18 ^ { \circ }$

Question 13

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

Accepted Answer

A)  $11.26$ 
B)  26 
C)  $6.5$ 
D)  $15.01$ 
A)  $11.26$ 
B)  26 
C)  $6.5$ 
D)  $15.01$

Question 14

Solve the equation.
-Solve $\sin \theta = \frac { 1 } { 2 }$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$.

Accepted Answer

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

Question 15

Graph the function.
-$y=4 \cos x-\sin 4 x$

Accepted Answer

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

Question 16

Evaluate without using a calculator by using ratios in a reference triangle.
-$\cos \frac { 5 \pi } { 3 }$

Accepted Answer

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

Question 17

Solve the problem.
-Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be $22 ^ { \circ } 56 ^ { \prime }$. He then drives 1 mile (1 mile $= 5280 \mathrm { ft }$ ) more and measures the angle of elevation to be $33 ^ { \circ } 9 ^ { \prime }$. Find the height of the mountain to the nearest foot.

Accepted Answer

A)  $6443 \mathrm { ft }$ 
B)  $634,295 \mathrm { ft }$ 
C)  $6343 \mathrm { ft }$ 
D)  $63,430 \mathrm { ft }$ 
A)  $6443 \mathrm { ft }$ 
B)  $634,295 \mathrm { ft }$ 
C)  $6343 \mathrm { ft }$ 
D)  $63,430 \mathrm { ft }$

Question 18

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema,
asymptotes, and end behavior.
-$$f ( x ) = \cos ^ { - 1 } ( 2 x )$$

Accepted Answer

Domain: @#LAT-DLM&
Range: @#LAT-DLM&
Continuous
De

Question 19

Solve the problem.
-Ignoring friction, the time, $t$ (in seconds), required for a block to slide down an inclined plane is given by the formula $t = \sqrt { \frac { 2 b } { g \sin \theta \cos \theta } }$ where $b$ is the length of the base in feet and $g = 32.2$ feet per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with a base of 12 feet at an angle of $35 ^ { \circ }$ ? Round your answer to three decimal places.

Accepted Answer

A)  $0.891 \mathrm { sec }$ 
B)  $7.147 \mathrm { sec }$ 
C)  $0.364 \mathrm { sec }$ 
D)  $1.26 \mathrm { sec }$ 
A)  $0.891 \mathrm { sec }$ 
B)  $7.147 \mathrm { sec }$ 
C)  $0.364 \mathrm { sec }$ 
D)  $1.26 \mathrm { sec }$

Question 20

Use a calculator to find the function value to four decimal places.
-$\cos 24.78 ^ { \circ }$

Accepted Answer

A)  $0.4191$ 
B)  $0.5767$ 
C)  $0.9079$ 
D)  $0.9959$ 
A)  $0.4191$ 
B)  $0.5767$ 
C)  $0.9079$ 
D)  $0.9959$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \cos \frac { x } { 5 } ; g ( x ) = \cos x$

Choose the graph which matches the function. - $f ( x ) = \sqrt { 11 } \cos 3.7 x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\arcsin 0.57$

Solve the problem. -When the angle of elevation of the sun is $\theta$ , a tree casts a shadow. Write a formula which expresses the length of the tree's shadow, $y$ , as a function of the angle $\theta$ and the height of the tree, $x$ .

Graph the function. - $y = - 3 \cos \frac { 1 } { 2 } x$

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - c = 37 \mathrm { B } = 28 ^ { \circ } 31 ^ { \circ }$ $c = 37$ $\mathrm { B } = 28 ^ { \circ } 31 ^ { \circ }$

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - \begin{array} { l } \mathrm { c } = 24 \\ \mathrm {~B} = 67 ^ { \circ } \end{array}$ =24 =6

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - \mathrm { C } = 14 B = 40 ^ { \circ }$ $\mathrm { C } = 14$ $B = 40 ^ { \circ }$

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

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. -4

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

Solve the equation. -Solve $\sin \theta = \frac { 1 } { 2 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$ .

Graph the function. - $y=4 \cos x-\sin 4 x$ $Graph the function. - y=4 \cos x-\sin 4 x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cos \frac { 5 \pi } { 3 }$

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = \cos ^ { - 1 } ( 2 x )$

Use a calculator to find the function value to four decimal places. - $\cos 24.78 ^ { \circ }$

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

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Exam 4: Trigonometric Functions

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - f(x)=cos⁡x5;g(x)=cos⁡xf ( x ) = \cos \frac { x } { 5 } ; g ( x ) = \cos xf(x)=cos5x​;g(x)=cosx

Choose the graph which matches the function. - f(x)=11cos⁡3.7xf ( x ) = \sqrt { 11 } \cos 3.7 xf(x)=11​cos3.7x

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - arcsin⁡0.57\arcsin 0.57arcsin0.57

Solve the problem. -When the angle of elevation of the sun is θ\thetaθ , a tree casts a shadow. Write a formula which expresses the length of the tree's shadow, yyy , as a function of the angle θ\thetaθ and the height of the tree, xxx .

Graph the function. - y=−3cos⁡12xy = - 3 \cos \frac { 1 } { 2 } xy=−3cos21​x

Solve the right triangle for all missing sides and angles to the nearest tenth. - c=37c = 37c=37 B=28∘31∘\mathrm { B } = 28 ^ { \circ } 31 ^ { \circ }B=28∘31∘

Solve the right triangle for all missing sides and angles to the nearest tenth. - =24 =6

Solve the right triangle for all missing sides and angles to the nearest tenth. - C=14\mathrm { C } = 14C=14 B=40∘B = 40 ^ { \circ }B=40∘

Graph the function. - y=−2sin⁡xy=-2 \sin xy=−2sinx