Question 1

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $$3.1416 \text { for } \pi$$
-$- 2.2$

Accepted Answer

A)  $- 126.15 ^ { \circ }$ 
B)  $- 252.00 ^ { \circ }$ 
C)  $- 252.10 ^ { \circ }$ 
D)  $- 126.05 ^ { \circ }$ 
A)  $- 126.15 ^ { \circ }$ 
B)  $- 252.00 ^ { \circ }$ 
C)  $- 252.10 ^ { \circ }$ 
D)  $- 126.05 ^ { \circ }$ D

Question 2

Find the exact circular function value.
-$$\cot \frac { - 11 \pi } { 6 }$$

Accepted Answer

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

Question 3

Graph the function.
-$y=-1-2 \cos x$

Accepted Answer

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

Question 4

Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-$$\mathrm { r } = 7.0 \mathrm { mi } , \theta = 268 ^ { \circ }$$

Accepted Answer

A)  $229.2 \mathrm { mi } ^ { 2 }$ 
B)  $38.3 \mathrm { mi } ^ { 2 }$ 
C)  $16.4 \mathrm { mi } ^ { 2 }$ 
D)  $114.6 \mathrm { mi } ^ { 2 }$ 
A)  $229.2 \mathrm { mi } ^ { 2 }$ 
B)  $38.3 \mathrm { mi } ^ { 2 }$ 
C)  $16.4 \mathrm { mi } ^ { 2 }$ 
D)  $114.6 \mathrm { mi } ^ { 2 }$

Question 5

Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-A pendulum swings through an angle of 16° each second. If the pendulum is 12 cm in length and 62) the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing?
Round to the nearest hundredth.

Accepted Answer

A)  $3.35 \mathrm {~cm} ^ { 2 }$ 
B)  $40.21 \mathrm {~cm} ^ { 2 }$ 
C)  $80.42 \mathrm {~cm} ^ { 2 }$ 
D)  $20.11 \mathrm {~cm} ^ { 2 }$ 
A)  $3.35 \mathrm {~cm} ^ { 2 }$ 
B)  $40.21 \mathrm {~cm} ^ { 2 }$ 
C)  $80.42 \mathrm {~cm} ^ { 2 }$ 
D)  $20.11 \mathrm {~cm} ^ { 2 }$

Question 6

Determine the equation of the graph.
-Determine the length of a pendulum that has a period of 2 seconds.

Accepted Answer

A)  $\frac { \pi ^ { 2 } } { 16 } \mathrm { ft }$ 
B)  $\frac { \pi } { 4 } \mathrm { ft }$ 
C)  $\frac { \pi } { 2 } \mathrm { ft }$ 
D)  $\frac { 32 } { \pi ^ { 2 } } \mathrm { ft }$ 
A)  $\frac { \pi ^ { 2 } } { 16 } \mathrm { ft }$ 
B)  $\frac { \pi } { 4 } \mathrm { ft }$ 
C)  $\frac { \pi } { 2 } \mathrm { ft }$ 
D)  $\frac { 32 } { \pi ^ { 2 } } \mathrm { ft }$

Question 7

Determine the equation of the graph.
-

Accepted Answer

A)  $y = 2 \csc x$ 
B)  $y = - 2 \sec x$ 
C)  $y = - \sec 2 x$ 
D)  $y = - \csc 2 x$ 
A)  $y = 2 \csc x$ 
B)  $y = - 2 \sec x$ 
C)  $y = - \sec 2 x$ 
D)  $y = - \csc 2 x$

Question 8

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$, are $486 \mathrm {~km}$ apart.

Accepted Answer

A)  $39.5 ^ { \circ } \mathrm { N }$ 
B)  $47.5 ^ { \circ } \mathrm { N }$ 
C)  $38.8 ^ { \circ } \mathrm { N }$ 
D)  $52.46 ^ { \circ } \mathrm { N }$ 
A)  $39.5 ^ { \circ } \mathrm { N }$ 
B)  $47.5 ^ { \circ } \mathrm { N }$ 
C)  $38.8 ^ { \circ } \mathrm { N }$ 
D)  $52.46 ^ { \circ } \mathrm { N }$

Question 9

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-The minute hand of a clock is 7 inches long. What distance does its tip move in 24 minutes? Give an exact answer.

Accepted Answer

A)  $\frac { 14 } { 5 } \pi$ in. 
B)  $\frac { 4 } { 35 } \pi$ in. 
C)  $\frac { 2 } { 35 } \pi$ in. 
D)  $\frac { 28 } { 5 } \pi \mathrm { in }$. 
A)  $\frac { 14 } { 5 } \pi$ in. 
B)  $\frac { 4 } { 35 } \pi$ in. 
C)  $\frac { 2 } { 35 } \pi$ in. 
D)  $\frac { 28 } { 5 } \pi \mathrm { in }$.

Question 10

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $$3.1416 \text { for } \pi$$
-2

Accepted Answer

A)  $228.98 ^ { \circ }$ 
B)  $114.59 ^ { \circ }$ 
C)  $229.18 ^ { \circ }$ 
D)  $114.79 ^ { \circ }$ 
A)  $228.98 ^ { \circ }$ 
B)  $114.59 ^ { \circ }$ 
C)  $229.18 ^ { \circ }$ 
D)  $114.79 ^ { \circ }$

Question 11

The figure shows an angle $$\theta$$ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of $\theta$
-Find $\tan \theta$

Accepted Answer

A)  $\frac { 12 } { 5 }$ 
B)  $- \frac { 13 } { 12 }$ 
C)  $- \frac { 5 } { 12 }$ 
D)  $- \frac { 12 } { 5 }$ 
A)  $\frac { 12 } { 5 }$ 
B)  $- \frac { 13 } { 12 }$ 
C)  $- \frac { 5 } { 12 }$ 
D)  $- \frac { 12 } { 5 }$

Question 12

The function graphed is of the form y $$y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$$ etermine the equation of the graph.
-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 $\left( \theta _ { 1 }  0 ^ { \circ } \right) , \mathrm { S }$ 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 $\mathrm { h } = 2.4 \mathrm { ft }$, $\alpha = 0.8 ^ { \circ } , \theta _ { 1 } = - 4 ^ { \circ } , \theta _ { 2 } = 3 ^ { \circ }$, and $S = 336 \mathrm { ft }$. Round your answer to the nearest foot.

Accepted Answer

A)  $543 \mathrm { ft }$ 
B)  $557 \mathrm { ft }$ 
C)  $588 \mathrm { ft }$ 
D)  $572 \mathrm { ft }$ 
A)  $543 \mathrm { ft }$ 
B)  $557 \mathrm { ft }$ 
C)  $588 \mathrm { ft }$ 
D)  $572 \mathrm { ft }$

Question 13

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$$\sin 0.1866$$

Accepted Answer

A)  1.0177 
B)  0.1855 
C)  0.9826 
D)  0.1888 
A)  1.0177 
B)  0.1855 
C)  0.9826 
D)  0.1888

Question 14

Convert the degree measure to radians, correct to four decimal places. $$3.1416 \text { for } \pi \text {. }$$
-$67 ^ { \circ }$

Accepted Answer

A)  $0.9694$ 
B)  $1.0694$ 
C)  $0.8694$ 
D)  $1.1694$ 
A)  $0.9694$ 
B)  $1.0694$ 
C)  $0.8694$ 
D)  $1.1694$

Question 15

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Suppose the tip of the minute hand of a clock is 3 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in $4.5$ hours. Give an exact answer.

Accepted Answer

A)  $12 \pi$ in. 
B)  $24 \pi \mathrm { in }$. 
C)  $27 \pi$ in. 
D)  $15 \pi$ in. 
A)  $12 \pi$ in. 
B)  $24 \pi \mathrm { in }$. 
C)  $27 \pi$ in. 
D)  $15 \pi$ in.

Question 16

Find the phase shift of the function.
-$$y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\pi$ units to the left 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $3 \pi$ units to the right 
A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\pi$ units to the left 
C)  $\frac { \pi } { 4 }$ units to the right 
D)  $3 \pi$ units to the right

Question 17

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 5.6 \cos 40 \pi \mathrm { t }$, where $t$ is time measured in seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one second).

Accepted Answer

A)  $\frac { 1 } { 40 }$ 
B)  $\frac { 1 } { 20 }$ 
C)  40 
D)  20 
A)  $\frac { 1 } { 40 }$ 
B)  $\frac { 1 } { 20 }$ 
C)  40 
D)  20

Question 18

Graph the function.
-$y=\frac{4}{3} \sec \left(\frac{3}{2} x-\frac{\pi}{6}\right)$

Accepted Answer

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

Question 19

Graph the function.
-$y=-\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{2}\right)$

Accepted Answer

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

Question 20

Solve the problem
-Let angle POQ be designated $\theta$. Angles $P Q R$ and VRQ are right angles. If $\theta = 41 ^ { \circ }$, find the length of PQ accurate to four decimal places.

Accepted Answer

A)  $0.6561$ 
B)  $0.8693$ 
C)  $1.5243$ 
D)  $0.7547$ 
A)  $0.6561$ 
B)  $0.8693$ 
C)  $1.5243$ 
D)  $0.7547$

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $3.1416 \text { for } \pi$ - $- 2.2$

Find the exact circular function value. - $\cot \frac { - 11 \pi } { 6 }$

Graph the function. - $y=-1-2 \cos x$ $Graph the function. - y=-1-2 \cos x$

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 7.0 \mathrm { mi } , \theta = 268 ^ { \circ }$

Determine the equation of the graph. -Determine the length of a pendulum that has a period of 2 seconds.

Determine the equation of the graph. -

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$ , are $486 \mathrm {~km}$ apart.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -The minute hand of a clock is 7 inches long. What distance does its tip move in 24 minutes? Give an exact answer.

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $3.1416 \text { for } \pi$ -2

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sin 0.1866$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $67 ^ { \circ }$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Suppose the tip of the minute hand of a clock is 3 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in $4.5$ hours. Give an exact answer.

Find the phase shift of the function. - $y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$

Graph the function. - $y=\frac{4}{3} \sec \left(\frac{3}{2} x-\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{4}{3} \sec \left(\frac{3}{2} x-\frac{\pi}{6}\right)$

Graph the function. - $y=-\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{1}{3} \cot \left(\frac{3}{5} x-\frac{\pi}{2}\right)$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 7: The Circular Functions and Their Graphs

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us 3.1416 for π3.1416 \text { for } \pi3.1416 for π - −2.2- 2.2−2.2

Find the exact circular function value. - cot⁡−11π6\cot \frac { - 11 \pi } { 6 }cot6−11π​

Graph the function. - y=−1−2cos⁡xy=-1-2 \cos xy=−1−2cosx

Find the area of a sector of a circle having radius r and central angle θ\thetaθ . If necessary, express the answer to the nearest tenth. - r=7.0mi,θ=268∘\mathrm { r } = 7.0 \mathrm { mi } , \theta = 268 ^ { \circ }r=7.0mi,θ=268∘