Question 1

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$275 ^ { \circ } 57 ^ { \prime } 58 ^ { \prime \prime }$

Accepted Answer

A)  $275.93 ^ { \circ }$ 
B)  $276.03 ^ { \circ }$ 
C)  $275.97 ^ { \circ }$ 
D)  $275.98 ^ { \circ }$ 
A)  $275.93 ^ { \circ }$ 
B)  $276.03 ^ { \circ }$ 
C)  $275.97 ^ { \circ }$ 
D)  $275.98 ^ { \circ }$

Question 2

Solve the problem.
-From a boat on the river below a dam, the angle of elevation to the top of the dam is $35 ^ { \circ } 18 ^ { \prime }$. If the dam is 371 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Accepted Answer

A)  $524 \mathrm { ft }$ 
B)  $494 \mathrm { ft }$ 
C)  $504 \mathrm { ft }$ 
D)  $514 \mathrm { ft }$ 
A)  $524 \mathrm { ft }$ 
B)  $494 \mathrm { ft }$ 
C)  $504 \mathrm { ft }$ 
D)  $514 \mathrm { ft }$

Question 3

Solve the equation.
-Solve $\tan \theta = \frac { 1 } { \sqrt { 3 } }$ for $\theta$, where $0 \leq \theta \leq \frac { \pi } { 2 }$.

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Solve the problem.
-A turntable rotates at 61 revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

A)  $\frac { 61 } { 60 } \pi$ radians/second 
B)  $\frac { 61 } { 30 } \pi$ radians/second 
C)  $\frac { 60 } { 61 } \pi$ radians/second 
D)  $\frac { 30 } { 61 } \pi$ radians/second 
A)  $\frac { 61 } { 60 } \pi$ radians/second 
B)  $\frac { 61 } { 30 } \pi$ radians/second 
C)  $\frac { 60 } { 61 } \pi$ radians/second 
D)  $\frac { 30 } { 61 } \pi$ radians/second

Question 6

Explain why the graphs of y = csc x and y = -k sin x will never intersect for any positive value of k.

Accepted Answer

In order for the graphs to int

Question 7

Solve the problem.
-To measure the width of a river, a surveyor starts at point A on one bank and walks 74 feet down the river to point B. He then measures the angle $\mathrm { ABC }$ to be $25 ^ { \circ } 34 ^ { \prime } 11 ^ { \prime \prime }$. Estimate the width of the river to the nearest foot. Se the figure below.

Accepted Answer

A)  35 feet 
B)  155 feet 
C)  32 feet 
D)  67 feet 
A)  35 feet 
B)  155 feet 
C)  32 feet 
D)  67 feet

Question 8

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

Accepted Answer

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

Question 9

Graph the function.
-$y=2.5 \cos \pi x$

Accepted Answer

A)  $2 \pi$ 
B)  $2.5$ 
C)  $\pi$ 
D)  2 
A)  $2 \pi$ 
B)  $2.5$ 
C)  $\pi$ 
D)  2

Question 10

Determine the sign (positive or negative) of the given value without use of a calculator.
-$$\tan \frac { 6 \pi } { 7 }$$

Accepted Answer

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

Question 11

Use the arc length formula and the given information to find the indicated quantity.
-$\mathrm { r } = 12$ in., $\theta = 14 \mathrm { rad }$; find $\mathrm { s }$

Accepted Answer

A)  $336 \mathrm { in }$. 
B)  $\frac { 7 } { 6 } \mathrm { in }$. 
C)  $\frac { 6 } { 7 } \mathrm { in }$. 
D)  $168 \mathrm { in }$. 
A)  $336 \mathrm { in }$. 
B)  $\frac { 7 } { 6 } \mathrm { in }$. 
C)  $\frac { 6 } { 7 } \mathrm { in }$. 
D)  $168 \mathrm { in }$.

Question 12

Find the exact value of the real number y.
-$$\mathrm { y } = \cot ^ { - 1 } \text { (1) }$$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-cos 0.2626

Accepted Answer

A)  1.035 
B)  0.9657 
C)  0.2596 
D)  0.2688 
A)  1.035 
B)  0.9657 
C)  0.2596 
D)  0.2688

Question 15

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

Accepted Answer

A)  $\frac { \sqrt { 51 } } { 7 }$ 
B)  $- \frac { \sqrt { 51 } } { 10 }$ 
C)  $- \frac { 10 \sqrt { 51 } } { 51 }$ 
D)  $- \frac { 7 \sqrt { 51 } } { 51 }$ 
A)  $\frac { \sqrt { 51 } } { 7 }$ 
B)  $- \frac { \sqrt { 51 } } { 10 }$ 
C)  $- \frac { 10 \sqrt { 51 } } { 51 }$ 
D)  $- \frac { 7 \sqrt { 51 } } { 51 }$

Question 16

Graph the function.
-$y=2.5 \sin 4 x$

Accepted Answer

A)  $2 \pi$ 
B)  $2.5$ 
C)  $\frac { \pi } { 2 }$ 
D)  $\frac { \pi } { 4 }$ 
A)  $2 \pi$ 
B)  $2.5$ 
C)  $\frac { \pi } { 2 }$ 
D)  $\frac { \pi } { 4 }$

Question 17

Evaluate without using a calculator by using ratios in a reference triangle.
-$\cot 120 ^ { \circ }$

Accepted Answer

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

Question 18

Find an algebraic expression equivalent to the given expression.
-$\sin ( \arctan u )$

Accepted Answer

A)  $\frac { \sqrt { \mathrm { u } ^ { 2 } - 1 } } { \mathrm { u } }$ 
B)  $\frac { \mathrm { u } \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } ^ { 2 } + 1 }$ 
C)  $\sqrt { u ^ { 2 } + 1 }$ 
D)  $\sqrt { \mathrm { u } ^ { 2 } - 1 }$ 
A)  $\frac { \sqrt { \mathrm { u } ^ { 2 } - 1 } } { \mathrm { u } }$ 
B)  $\frac { \mathrm { u } \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } ^ { 2 } + 1 }$ 
C)  $\sqrt { u ^ { 2 } + 1 }$ 
D)  $\sqrt { \mathrm { u } ^ { 2 } - 1 }$

Question 19

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.
-Amplitude 5, period $\frac { \pi } { 2 }$, point $( 0,0 )$

Accepted Answer

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

Question 20

Solve the problem.
-If the radius of the earth is approximately 3960 miles, what is the linear speed of a point on the equator in miles per hour. Round your answer to the nearest mph.

Accepted Answer

A)  $1037 \mathrm { mph }$ 
B)  $1681 \mathrm { mph }$ 
C)  $2073 \mathrm { mph }$ 
D)  $840 \mathrm { mph }$ 
A)  $1037 \mathrm { mph }$ 
B)  $1681 \mathrm { mph }$ 
C)  $2073 \mathrm { mph }$ 
D)  $840 \mathrm { mph }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $275 ^ { \circ } 57 ^ { \prime } 58 ^ { \prime \prime }$

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $35 ^ { \circ } 18 ^ { \prime }$ . If the dam is 371 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Solve the equation. -Solve $\tan \theta = \frac { 1 } { \sqrt { 3 } }$ for $\theta$ , where $0 \leq \theta \leq \frac { \pi } { 2 }$ .

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

Solve the problem. -A turntable rotates at 61 revolutions per minute. What is its angular speed in radians per second?

Explain why the graphs of y = csc x and y = -k sin x will never intersect for any positive value of k.

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

Graph the function. - $y=2.5 \cos \pi x$ $Graph the function. - y=2.5 \cos \pi x$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan \frac { 6 \pi } { 7 }$

Use the arc length formula and the given information to find the indicated quantity. - $\mathrm { r } = 12$ in., $\theta = 14 \mathrm { rad }$ ; find $\mathrm { s }$

Find the exact value of the real number y. - $\mathrm { y } = \cot ^ { - 1 } \text { (1) }$

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

Use a calculator to evaluate the function. Round your answer to 4 decimal places. -cos 0.2626

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

Graph the function. - $y=2.5 \sin 4 x$ $Graph the function. - y=2.5 \sin 4 x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cot 120 ^ { \circ }$

Find an algebraic expression equivalent to the given expression. - $\sin ( \arctan u )$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 5, period $\frac { \pi } { 2 }$ , point $( 0,0 )$

Solve the problem. -If the radius of the earth is approximately 3960 miles, what is the linear speed of a point on the equator in miles per hour. Round your answer to the nearest mph.

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

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 275∘57′58′′275 ^ { \circ } 57 ^ { \prime } 58 ^ { \prime \prime }275∘57′58′′

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 35∘18′35 ^ { \circ } 18 ^ { \prime }35∘18′ . If the dam is 371 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Solve the equation. -Solve tan⁡θ=13\tan \theta = \frac { 1 } { \sqrt { 3 } }tanθ=3​1​ for θ\thetaθ , where 0≤θ≤π20 \leq \theta \leq \frac { \pi } { 2 }0≤θ≤2π​ .

Solve for x in the given interval. - sec⁡x=−2,π≤x≤3π2\sec x = - 2 , \pi \leq x \leq \frac { 3 \pi } { 2 }secx=−2,π≤x≤23π​

Solve the problem. -A turntable rotates at 61 revolutions per minute. What is its angular speed in radians per second?

Explain why the graphs of y = csc x and y = -k sin x will never intersect for any positive value of k.

Graph the function. - y=43cos⁡23xy=\frac{4}{3} \cos \frac{2}{3} xy=34​cos32​x

Graph the function. - y=2.5cos⁡πxy=2.5 \cos \pi xy=2.5cosπx

Determine the sign (positive or negative) of the given value without use of a calculator. - tan⁡6π7\tan \frac { 6 \pi } { 7 }tan76π​

Use the arc length formula and the given information to find the indicated quantity. - r=12\mathrm { r } = 12r=12 in., θ=14rad\theta = 14 \mathrm { rad }θ=14rad ; find s\mathrm { s }s

Find the exact value of the real number y. - y=cot⁡−1 (1) \mathrm { y } = \cot ^ { - 1 } \text { (1) }y=cot−1 (1)

Solve for x in the given interval. - sec⁡x=−233,π2≤x≤π\sec x = - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pisecx=−323​​,2π​≤x≤π

Use a calculator to evaluate the function. Round your answer to 4 decimal places. -cos 0.2626

Evaluate without using a calculator. - cot⁡γ\cot \gammacotγ , if csc⁡γ=−107\csc \gamma = - \frac { 10 } { 7 }cscγ=−710​ and cos⁡γ<0\cos \gamma < 0cosγ<0

Graph the function. - y=2.5sin⁡4xy=2.5 \sin 4 xy=2.5sin4x

Evaluate without using a calculator by using ratios in a reference triangle. - cot⁡120∘\cot 120 ^ { \circ }cot120∘

Find an algebraic expression equivalent to the given expression. - sin⁡(arctan⁡u)\sin ( \arctan u )sin(arctanu)

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 5, period π2\frac { \pi } { 2 }2π​ , point (0,0)( 0,0 )(0,0)

Solve the problem. -If the radius of the earth is approximately 3960 miles, what is the linear speed of a point on the equator in miles per hour. Round your answer to the nearest mph.

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

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $275 ^ { \circ } 57 ^ { \prime } 58 ^ { \prime \prime }$

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $35 ^ { \circ } 18 ^ { \prime }$ . If the dam is 371 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Solve the equation. -Solve $\tan \theta = \frac { 1 } { \sqrt { 3 } }$ for $\theta$ , where $0 \leq \theta \leq \frac { \pi } { 2 }$ .

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

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

Graph the function. - $y=2.5 \cos \pi x$ $Graph the function. - y=2.5 \cos \pi x$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan \frac { 6 \pi } { 7 }$

Use the arc length formula and the given information to find the indicated quantity. - $\mathrm { r } = 12$ in., $\theta = 14 \mathrm { rad }$ ; find $\mathrm { s }$

Find the exact value of the real number y. - $\mathrm { y } = \cot ^ { - 1 } \text { (1) }$

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

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

Graph the function. - $y=2.5 \sin 4 x$ $Graph the function. - y=2.5 \sin 4 x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cot 120 ^ { \circ }$

Find an algebraic expression equivalent to the given expression. - $\sin ( \arctan u )$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 5, period $\frac { \pi } { 2 }$ , point $( 0,0 )$