Question 1

Find the exact circular function value.
-$\tan \frac { 7 \pi } { 6 }$

Accepted Answer

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

Question 2

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

Accepted Answer

A)  $\frac { 25 } { 24 }$ 
B)  $- \frac { 25 } { 24 }$ 
C)  $- \frac { 25 } { 7 }$ 
D)  $\frac { 24 } { 7 }$ 
A)  $\frac { 25 } { 24 }$ 
B)  $- \frac { 25 } { 24 }$ 
C)  $- \frac { 25 } { 7 }$ 
D)  $\frac { 24 } { 7 }$

Question 3

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\sin 0.2721$

Accepted Answer

A)  $0.9632$ 
B)  $1.0382$ 
C)  $0.2688$ 
D)  $0.2790$ 
A)  $0.9632$ 
B)  $1.0382$ 
C)  $0.2688$ 
D)  $0.2790$

Question 4

Solve the problem.
-An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of $\frac { 1 } { 3 }$ radian has been covered, what is the linear speed of the object?

Accepted Answer

A)  $\frac { 38 } { 27 } \mathrm {~cm}$ per sec 
B)  $\frac { 19 } { 27 } \mathrm {~cm}$ per sec 
C)  $19 \mathrm {~cm}$ per sec 
D)  $57 \mathrm {~cm}$ per sec 
A)  $\frac { 38 } { 27 } \mathrm {~cm}$ per sec 
B)  $\frac { 19 } { 27 } \mathrm {~cm}$ per sec 
C)  $19 \mathrm {~cm}$ per sec 
D)  $57 \mathrm {~cm}$ per sec

Question 5

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 $44 ^ { \circ }$ ? Round your answer to three decimal places.

Accepted Answer

A)  $6.93 \mathrm { sec }$ 
B)  $0.353 \mathrm { sec }$ 
C)  $0.864 \mathrm { sec }$ 
D)  $1.221 \mathrm { sec }$ 
A)  $6.93 \mathrm { sec }$ 
B)  $0.353 \mathrm { sec }$ 
C)  $0.864 \mathrm { sec }$ 
D)  $1.221 \mathrm { sec }$

Question 6

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 $\left( \theta _ { 1 }  0 ^ { \circ } \right) , \mathrm { S }$ 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 $h = 1.6 \mathrm { ft }$, $\alpha = 0.8 ^ { \circ } , \theta _ { 1 } = - 5 ^ { \circ } , \theta _ { 2 } = 1 ^ { \circ }$, and $S = 336 \mathrm { ft }$. Round your answer to the nearest foot.

Accepted Answer

A)  $525 \mathrm { ft }$ 
B)  $553 \mathrm { ft }$ 
C)  $568 \mathrm { ft }$ 
D)  $538 \mathrm { ft }$ 
A)  $525 \mathrm { ft }$ 
B)  $553 \mathrm { ft }$ 
C)  $568 \mathrm { ft }$ 
D)  $538 \mathrm { ft }$

Question 7

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

Accepted Answer

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

Question 8

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$$- 262 ^ { \circ } 58 ^ { \prime }$$

Accepted Answer

A)  $- 4.5696$ 
B)  $- 4.5596$ 
C)  $- 4.5796$ 
D)  $- 4.5896$ 
A)  $- 4.5696$ 
B)  $- 4.5596$ 
C)  $- 4.5796$ 
D)  $- 4.5896$

Question 9

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

Accepted Answer

A)  $\frac { 7 } { 25 }$ 
B)  $\frac { 7 } { 24 }$ 
C)  $- \frac { 7 } { 25 }$ 
D)  $- \frac { 24 } { 25 }$ 
A)  $\frac { 7 } { 25 }$ 
B)  $\frac { 7 } { 24 }$ 
C)  $- \frac { 7 } { 25 }$ 
D)  $- \frac { 24 } { 25 }$

Question 10

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$86.9152 ^ { \circ }$

Accepted Answer

A)  $1.7170$ 
B)  $1.5170$ 
C)  $1.6170$ 
D)  $1.8170$ 
A)  $1.7170$ 
B)  $1.5170$ 
C)  $1.6170$ 
D)  $1.8170$

Question 11

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.
-

Accepted Answer

A)  $y = 2 \cos ( 3 x )$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = - 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = - 2 \sin ( 3 x )$ 
A)  $y = 2 \cos ( 3 x )$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = - 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = - 2 \sin ( 3 x )$

Question 12

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

Accepted Answer

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

Question 13

Solve the problem.
-Let angle $P O Q$ be designated $\theta$. Angles $P Q R$ and $V R Q$ are right angles. If $\theta = 45 ^ { \circ }$, find the exact length of US.

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  0 
C)  1 
D)  $\sqrt { 2 }$ 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  0 
C)  1 
D)  $\sqrt { 2 }$

Question 14

Determine the equation of the graph.
-

Accepted Answer

A)  $y = - \sec 2 x$ 
B)  $y = \sec \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = \sec 2 x$ 
D)  $y = - \sec \left( \frac { 1 } { 2 } x \right)$ 
A)  $y = - \sec 2 x$ 
B)  $y = \sec \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = \sec 2 x$ 
D)  $y = - \sec \left( \frac { 1 } { 2 } x \right)$

Question 15

Solve the problem.
-The minute hand of a clock is 14 inches long. What distance does its tip move in 23 minutes? Give an exact answer.

Accepted Answer

A)  $\frac { 161 } { 30 } \pi \mathrm { in }$. 
B)  $\frac { 23 } { 840 } \pi \mathrm { in }$. 
C)  $\frac { 23 } { 420 } \pi \mathrm { in }$. 
D)  $\frac { 161 } { 15 } \pi \mathrm { in }$. 
A)  $\frac { 161 } { 30 } \pi \mathrm { in }$. 
B)  $\frac { 23 } { 840 } \pi \mathrm { in }$. 
C)  $\frac { 23 } { 420 } \pi \mathrm { in }$. 
D)  $\frac { 161 } { 15 } \pi \mathrm { in }$.

Question 16

Solve the problem.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }$, where $t$ is time measured in seconds. Find the amplitude.

Accepted Answer

A)  $3.1$ 
B)  140 
C)  $6.2$ 
D)  $140 \pi$ 
A)  $3.1$ 
B)  140 
C)  $6.2$ 
D)  $140 \pi$

Question 17

Solve the problem.
-A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Accepted Answer

A)  $s ( t ) = 2 \sin \sqrt { 6 } t$ 
B)  $s ( t ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 12 } } t$ 
C)  $s ( t ) = 2 \sin \sqrt { \frac { 1 } { 6 } } t$ 
D)  $s ( t ) = 6 \sin \sqrt { 2 } t$ 
A)  $s ( t ) = 2 \sin \sqrt { 6 } t$ 
B)  $s ( t ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 12 } } t$ 
C)  $s ( t ) = 2 \sin \sqrt { \frac { 1 } { 6 } } t$ 
D)  $s ( t ) = 6 \sin \sqrt { 2 } t$

Question 18

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-$\sin \mathrm { s } = 0.8454$

Accepted Answer

A)  $- 0.8657$ 
B)  $0.2759$ 
C)  $1.0073$ 
D)  $2.1343$ 
A)  $- 0.8657$ 
B)  $0.2759$ 
C)  $1.0073$ 
D)  $2.1343$

Question 19

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

Accepted Answer

A)  $- \frac { 7 } { 24 }$ 
B)  $\frac { 7 } { 25 }$ 
C)  $\frac { 24 } { 25 }$ 
D)  $- \frac { 24 } { 25 }$ 
A)  $- \frac { 7 } { 24 }$ 
B)  $\frac { 7 } { 25 }$ 
C)  $\frac { 24 } { 25 }$ 
D)  $- \frac { 24 } { 25 }$

Question 20

Solve the problem.
-A sensor light installed on the edge of a home can detect motion for a distance of $50 \mathrm { ft }$. in front and with a range of motion of $238 ^ { \circ }$. Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

Accepted Answer

A)  $5192.35 \mathrm { ft } ^ { 2 }$ 
B)  $10,384.81 \mathrm { ft } ^ { 2 }$ 
C)  $10,384.71 \mathrm { ft } ^ { 2 }$ 
D)  $5192.25 \mathrm { ft } ^ { 2 }$ 
A)  $5192.35 \mathrm { ft } ^ { 2 }$ 
B)  $10,384.81 \mathrm { ft } ^ { 2 }$ 
C)  $10,384.71 \mathrm { ft } ^ { 2 }$ 
D)  $5192.25 \mathrm { ft } ^ { 2 }$

Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\sin 0.2721$

Solve the problem. -An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of $\frac { 1 } { 3 }$ radian has been covered, what is the linear speed of the object?

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

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $- 262 ^ { \circ } 58 ^ { \prime }$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $86.9152 ^ { \circ }$

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

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

Determine the equation of the graph. -

Solve the problem. -The minute hand of a clock is 14 inches long. What distance does its tip move in 23 minutes? Give an exact answer.

Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.1 \cos 140 \pi \mathrm { t }$ , where $t$ is time measured in seconds. Find the amplitude.

Solve the problem. -A spring with a spring constant of 6 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\sin \mathrm { s } = 0.8454$

Solve the problem. -A sensor light installed on the edge of a home can detect motion for a distance of $50 \mathrm { ft }$ . in front and with a range of motion of $238 ^ { \circ }$ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

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

Review of Basic Concepts

Filters

Exam 6: The Circular Functions and Their Graphs

Find the exact circular function value. - tan⁡7π6\tan \frac { 7 \pi } { 6 }tan67π​

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find csc⁡θ\csc \thetacscθ .

Use a table or a calculator to evaluate the function. Round to four decimal places. - sin⁡0.2721\sin 0.2721sin0.2721

Solve the problem. -An object is spinning around a circle with a radius of 19 centimeters. If in 9 seconds a central angle of 13\frac { 1 } { 3 }31​ radian has been covered, what is the linear speed of the object?

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

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - −262∘58′- 262 ^ { \circ } 58 ^ { \prime }−262∘58′

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find cos⁡θ\cos \thetacosθ

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 86.9152∘86.9152 ^ { \circ }86.9152∘