Question 1

Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = 2 x + \sin 5 x$$

Accepted Answer

A)  Not periodic 
B)  $2 \pi$ 
C)  $10 \pi$ 
D)  $\frac { 2 \pi } { 5 }$ 
A)  Not periodic 
B)  $2 \pi$ 
C)  $10 \pi$ 
D)  $\frac { 2 \pi } { 5 }$

Question 2

Solve the problem.
-The total sales in dollars of some small businesses fluctuates according to the equation $S = A + B \sin \pi x / 6$, where $x$ is the time in months, with $x = 1$ corresponding to January, $A = 5800$, and $B = 2600$. Determine the month with the greatest total sales and give the sales in that month.

Accepted Answer

A)  September; $\$ 3200$ 
B)  June; $\$ 5800$ 
C)  March; $\$ 8400$ 
D)  December; $\$ 8400$ 
A)  September; $\$ 3200$ 
B)  June; $\$ 5800$ 
C)  March; $\$ 8400$ 
D)  December; $\$ 8400$

Question 3

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$11.52 ^ { \circ }$

Accepted Answer

A)  $0.1005$ 
B)  $0.2011$ 
C)  $0.064$ 
D)  $0.134$ 
A)  $0.1005$ 
B)  $0.2011$ 
C)  $0.064$ 
D)  $0.134$

Question 4

Solve the problem.
-On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is $35 \mathrm {~m}$ long and the shadow is $28 \mathrm {~m}$, how tall is the flag pole?

Accepted Answer

A)  $21 \mathrm {~m}$ 
B)  $49 \mathrm {~m}$ 
C)  $63 \mathrm {~m}$ 
D)  $45 \mathrm {~m}$ 
A)  $21 \mathrm {~m}$ 
B)  $49 \mathrm {~m}$ 
C)  $63 \mathrm {~m}$ 
D)  $45 \mathrm {~m}$

Question 5

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$c=9$
$A = 56 ^ { \circ }$

Accepted Answer

A)  $\mathrm { B } = 34 ^ { \circ } , \mathrm { a } = 5 , \mathrm {~b} = 7.5$ 
B)  $B = 34 ^ { \circ } , a = 13.3 , b = 7.5$ 
C)  $B = 34 ^ { \circ } , a = 5 , b = 13.3$ 
D)  $B = 34 ^ { \circ } , a = 7.5 , b = 5$ 
A)  $\mathrm { B } = 34 ^ { \circ } , \mathrm { a } = 5 , \mathrm {~b} = 7.5$ 
B)  $B = 34 ^ { \circ } , a = 13.3 , b = 7.5$ 
C)  $B = 34 ^ { \circ } , a = 5 , b = 13.3$ 
D)  $B = 34 ^ { \circ } , a = 7.5 , b = 5$

Question 6

Evaluate.
-$$\sin \left( \frac { \pi } { 3 } + 258 \pi \right)$$

Accepted Answer

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

Question 7

Use the arc length formula and the given information to find the indicated quantity.
-$\mathrm { s } = 10 \mathrm {~m} , \mathrm { r } = 7 \mathrm {~m}$; find $\theta$

Accepted Answer

A)  $140 \mathrm { rad }$ 
B)  $\frac { 10 } { 7 } \mathrm { rad }$ 
C)  $70 \mathrm { rad }$ 
D)  $\frac { 7 } { 10 } \mathrm { rad }$ 
A)  $140 \mathrm { rad }$ 
B)  $\frac { 10 } { 7 } \mathrm { rad }$ 
C)  $70 \mathrm { rad }$ 
D)  $\frac { 7 } { 10 } \mathrm { rad }$

Question 8

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$51 ^ { \circ } 26 ^ { \prime }$

Accepted Answer

A)  $51.26 ^ { \circ }$ 
B)  $52.43 ^ { \circ }$ 
C)  $51.43 ^ { \circ }$ 
D)  $51.52 ^ { \circ }$ 
A)  $51.26 ^ { \circ }$ 
B)  $52.43 ^ { \circ }$ 
C)  $51.43 ^ { \circ }$ 
D)  $51.52 ^ { \circ }$

Question 9

Solve the problem.
-Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is $6400 \mathrm {~km}$. City A, $59 ^ { \circ } \mathrm { N }$ and city B, $25 ^ { \circ } \mathrm { N }$

Accepted Answer

A)  $3798 \mathrm {~km}$ 
B)  $3882 \mathrm {~km}$ 
C)  $3739 \mathrm {~km}$ 
D)  $3823 \mathrm {~km}$ 
A)  $3798 \mathrm {~km}$ 
B)  $3882 \mathrm {~km}$ 
C)  $3739 \mathrm {~km}$ 
D)  $3823 \mathrm {~km}$

Question 10

Describe the end behavior of the function.
-$$f ( x ) = e ^ { - x } \cos 4 x$$

Accepted Answer

A)  $\lim _ { x \rightarrow\infty } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
C)  $\lim _ { x \rightarrow } f ( x ) = 0$ 
D)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
A)  $\lim _ { x \rightarrow\infty } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
C)  $\lim _ { x \rightarrow } f ( x ) = 0$ 
D)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$

Question 11

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = - 9.5 \sin x ; g ( x ) = \sin x$$

Accepted Answer

A)  Vertical stretch by a factor of $9.5$, reflection across $y$-axis 
B)  Horizontal stretch by a factor of $9.5$, reflection across $x$-axis 
C)  Vertical stretch by a factor of $9.5$, reflection across $x$-axis 
D)  Horizontal stretch by a factor of $9.5$, reflection across $\mathrm { y }$-axis 
A)  Vertical stretch by a factor of $9.5$, reflection across $y$-axis 
B)  Horizontal stretch by a factor of $9.5$, reflection across $x$-axis 
C)  Vertical stretch by a factor of $9.5$, reflection across $x$-axis 
D)  Horizontal stretch by a factor of $9.5$, reflection across $\mathrm { y }$-axis

Question 12

Use a calculator to graph the function.
-$y=\sqrt{\sin ^{2} x}$

Accepted Answer

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

Question 13

Use a calculator to find the function value to four decimal places.
-$\cos 21.1 ^ { \circ }$

Accepted Answer

A)  $0.9330$ 
B)  $0.3859$ 
C)  $0.6285$ 
D)  $0.3600$ 
A)  $0.9330$ 
B)  $0.3859$ 
C)  $0.6285$ 
D)  $0.3600$

Question 14

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric
graph.
-$$f ( x ) = 6 \cos ^ { - 1 } 8 x$$

Accepted Answer

A)  Vertical stretch by a factor of 6 and horizontal shrink by a factor of $\frac { 1 } { 8 }$ 
B)  Vertical stretch by a factor of 8 and horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
C)  Vertical translation up 6 units and horizontal translation to the right 8 units 
D)  Vertical stretch by a factor of 6 and horizontal stretch by a factor of 8 
A)  Vertical stretch by a factor of 6 and horizontal shrink by a factor of $\frac { 1 } { 8 }$ 
B)  Vertical stretch by a factor of 8 and horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
C)  Vertical translation up 6 units and horizontal translation to the right 8 units 
D)  Vertical stretch by a factor of 6 and horizontal stretch by a factor of 8

Question 15

Solve.
-In an electric circuit, the electromotive force is defined as $\mathrm { V } = \cos 2 \pi t$, where $t$ is time in seconds. Solve the equation for $t$.

Accepted Answer

A)  $t = 2 \pi \cos V$ 
B)  $t = \frac { 1 } { 2 \pi }$ Arccos V 
C)  $t = 2 \pi$ Arccos $V$ 
D)  $t = \frac { 1 } { 2 \pi } \cos V$ 
A)  $t = 2 \pi \cos V$ 
B)  $t = \frac { 1 } { 2 \pi }$ Arccos V 
C)  $t = 2 \pi$ Arccos $V$ 
D)  $t = \frac { 1 } { 2 \pi } \cos V$

Question 16

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
-$$\frac { 11 \pi } { 2 }$$

Accepted Answer

A)  $990 ^ { \circ }$ 
B)  $32.73 \pi ^ { \circ }$ 
C)  $1980 ^ { \circ }$ 
D)  $163.64 ^ { \circ }$ 
A)  $990 ^ { \circ }$ 
B)  $32.73 \pi ^ { \circ }$ 
C)  $1980 ^ { \circ }$ 
D)  $163.64 ^ { \circ }$

Question 17

Choose the point on the terminal side of .
-$$\theta = \frac { \pi } { 4 }$$

Accepted Answer

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

Question 18

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
-$- \pi / 2$

Accepted Answer

A)  $- 90 ^ { \circ }$ 
B)  $- 1.57 ^ { \circ }$ 
C)  $- 90 \pi ^ { \circ }$ 
D)  $- ( \pi / 2 ) ^ { \circ }$ 
A)  $- 90 ^ { \circ }$ 
B)  $- 1.57 ^ { \circ }$ 
C)  $- 90 \pi ^ { \circ }$ 
D)  $- ( \pi / 2 ) ^ { \circ }$

Question 19

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

Accepted Answer

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

Question 20

Solve the problem.
-When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $31 ^ { \circ }$ 31'. If Joey is known to be standing 30 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Accepted Answer

A)  $20 \mathrm { ft }$ 
B)  $22 \mathrm { ft }$ 
C)  $24 \mathrm { ft }$ 
D)  $18 \mathrm { ft }$ 
A)  $20 \mathrm { ft }$ 
B)  $22 \mathrm { ft }$ 
C)  $24 \mathrm { ft }$ 
D)  $18 \mathrm { ft }$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 2 x + \sin 5 x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $11.52 ^ { \circ }$

Solve the problem. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is $35 \mathrm {~m}$ long and the shadow is $28 \mathrm {~m}$ , how tall is the flag pole?

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - c=9 A = 56 ^ { \circ }$ $c=9$ $A = 56 ^ { \circ }$

Evaluate. - $\sin \left( \frac { \pi } { 3 } + 258 \pi \right)$

Use the arc length formula and the given information to find the indicated quantity. - $\mathrm { s } = 10 \mathrm {~m} , \mathrm { r } = 7 \mathrm {~m}$ ; find $\theta$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $51 ^ { \circ } 26 ^ { \prime }$

Solve the problem. -Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a north-south line and that the radius of the earth is $6400 \mathrm {~km}$ . City A, $59 ^ { \circ } \mathrm { N }$ and city B, $25 ^ { \circ } \mathrm { N }$

Describe the end behavior of the function. - $f ( x ) = e ^ { - x } \cos 4 x$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = - 9.5 \sin x ; g ( x ) = \sin x$

Use a calculator to graph the function. - $y=\sqrt{\sin ^{2} x}$ $Use a calculator to graph the function. - y=\sqrt{\sin ^{2} x}$

Use a calculator to find the function value to four decimal places. - $\cos 21.1 ^ { \circ }$

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - $f ( x ) = 6 \cos ^ { - 1 } 8 x$

Solve. -In an electric circuit, the electromotive force is defined as $\mathrm { V } = \cos 2 \pi t$ , where $t$ is time in seconds. Solve the equation for $t$ .

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - $\frac { 11 \pi } { 2 }$

Choose the point on the terminal side of . - $\theta = \frac { \pi } { 4 }$

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - $- \pi / 2$

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

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $31 ^ { \circ }$ 31'. If Joey is known to be standing 30 feet from the base of the tree, how tall is the tree (to the nearest foot)?

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

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 4: Trigonometric Functions

Determine whether the function is periodic. If it is periodic, find the period. - f(x)=2x+sin⁡5xf ( x ) = 2 x + \sin 5 xf(x)=2x+sin5x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 11.52∘11.52 ^ { \circ }11.52∘

Solve the problem. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 35 m35 \mathrm {~m}35 m long and the shadow is 28 m28 \mathrm {~m}28 m , how tall is the flag pole?

Solve the right triangle for all missing sides and angles to the nearest tenth. - c=9c=9c=9 A=56∘A = 56 ^ { \circ }A=56∘

Evaluate. - sin⁡(π3+258π)\sin \left( \frac { \pi } { 3 } + 258 \pi \right)sin(3π​+258π)

Use the arc length formula and the given information to find the indicated quantity. - s=10 m,r=7 m\mathrm { s } = 10 \mathrm {~m} , \mathrm { r } = 7 \mathrm {~m}s=10 m,r=7 m ; find θ\thetaθ

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 51∘26′51 ^ { \circ } 26 ^ { \prime }51∘26′

Describe the end behavior of the function. - f(x)=e−xcos⁡4xf ( x ) = e ^ { - x } \cos 4 xf(x)=e−xcos4x

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - f(x)=−9.5sin⁡x;g(x)=sin⁡xf ( x ) = - 9.5 \sin x ; g ( x ) = \sin xf(x)=−9.5sinx;g(x)=sinx

Use a calculator to graph the function. - y=sin⁡2xy=\sqrt{\sin ^{2} x}y=sin2x​

Use a calculator to find the function value to four decimal places. - cos⁡21.1∘\cos 21.1 ^ { \circ }cos21.1∘

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - f(x)=6cos⁡−18xf ( x ) = 6 \cos ^ { - 1 } 8 xf(x)=6cos−18x

Solve. -In an electric circuit, the electromotive force is defined as V=cos⁡2πt\mathrm { V } = \cos 2 \pi tV=cos2πt , where ttt is time in seconds. Solve the equation for ttt .

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - 11π2\frac { 11 \pi } { 2 }211π​

Choose the point on the terminal side of . - θ=π4\theta = \frac { \pi } { 4 }θ=4π​

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - −π/2- \pi / 2−π/2

Graph the function. - y=3sec⁡xy=3 \sec xy=3secx

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 31∘31 ^ { \circ }31∘ 31'. If Joey is known to be standing 30 feet from the base of the tree, how tall is the tree (to the nearest foot)?