Question 1

Find the exact value of the expression.
-$\csc \left( - 960 ^ { \circ } \right)$

Accepted Answer

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

Question 2

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
-$\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

Accepted Answer

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

Question 3

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
B)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
C)  $95 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
A)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
B)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
C)  $95 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $100 ^ { \circ }$ and $80 ^ { \circ }$

Question 4

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\cos 205 ^ { \circ } 3 ^ { \prime }$

Accepted Answer

A)  $- 0.9059386$ 
B)  $- 0.5529693$ 
C)  $- 0.4529693$ 
D)  $- 0.7059386$ 
A)  $- 0.9059386$ 
B)  $- 0.5529693$ 
C)  $- 0.4529693$ 
D)  $- 0.7059386$

Question 5

Solve the problem.
-Find $\mathrm { h }$ as indicated in the figure. Round to the nearest meter.

Accepted Answer

A)  $28 \mathrm {~m}$ 
B)  $63 \mathrm {~m}$ 
C)  $143 \mathrm {~m}$ 
D)  $43 \mathrm {~m}$ 
A)  $28 \mathrm {~m}$ 
B)  $63 \mathrm {~m}$ 
C)  $143 \mathrm {~m}$ 
D)  $43 \mathrm {~m}$

Question 6

Find the exact value of the expression.
-$\cos 2040 ^ { \circ }$

Accepted Answer

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

Question 7

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
-Find $\tan \mathrm { B }$ when $\mathrm { a } = 24$ and $\mathrm { c } = 25$.

Accepted Answer

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

Question 8

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { B } = 74 ^ { \circ } 24 ^ { \prime } , \mathrm { b } = 11 \mathrm {~km}$$
Round side lengths to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 11.4 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
B)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 40.9 \mathrm {~km} ; \mathrm { a } = 11.4 \mathrm {~km}$ 
C)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 40.9 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
D)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 11.4 \mathrm {~km} ; \mathrm { a } = 40.5 \mathrm {~km}$ 
A)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 11.4 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
B)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 40.9 \mathrm {~km} ; \mathrm { a } = 11.4 \mathrm {~km}$ 
C)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 40.9 \mathrm {~km} ; \mathrm { a } = 3.1 \mathrm {~km}$ 
D)  $\mathrm { A } = 15 ^ { \circ } 36 ^ { \prime } ; \mathrm { c } = 11.4 \mathrm {~km} ; \mathrm { a } = 40.5 \mathrm {~km}$

Question 9

An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of θ. Do not use a calculator.
-$- 7 x - 5 y = 0 , x \leq 0 ; \quad$ Find $\sec \theta$

Accepted Answer

A)  $- \frac { 5 } { 7 }$ 
B)  $- \frac { 5 \sqrt { 74 } } { 74 }$ 
C)  $ - \frac { 7 } { 5 }$ 
D)  $- \frac { \sqrt { 74 } } { 5 }$ 
A)  $- \frac { 5 } { 7 }$ 
B)  $- \frac { 5 \sqrt { 74 } } { 74 }$ 
C)  $ - \frac { 7 } { 5 }$ 
D)  $- \frac { \sqrt { 74 } } { 5 }$

Question 10

Solve the right triangle.
-$$\mathrm { A } = 15 ^ { \circ } 19 ^ { \prime } , \mathrm { c } = 295 \mathrm { ft } , \mathrm { C } = 90 ^ { \circ }$$
Round side lengths to two decimal places, if necessary.

Accepted Answer

A)  $\mathrm { B } = 74 ^ { \circ } 40 ^ { \prime } , \mathrm { a } = 81.13 \mathrm { ft } , \mathrm { b } = 285.72 \mathrm { ft }$ 
B)  $\mathrm { B } = 74 ^ { \circ } 41 ^ { \prime } , \mathrm { a } = 77.36 \mathrm { ft } , \mathrm { b } = 283.63 \mathrm { ft }$ 
C)  $B = 74 ^ { \circ } 41 ^ { \prime } , \mathrm { a } = 77.93 \mathrm { ft } , \mathrm { b } = 284.52 \mathrm { ft }$ 
D)  $B = 75 ^ { \circ } 40 ^ { \prime } , \mathrm { a } = 77.93 \mathrm { ft } , \mathrm { b } = 280.52 \mathrm { ft }$ 
A)  $\mathrm { B } = 74 ^ { \circ } 40 ^ { \prime } , \mathrm { a } = 81.13 \mathrm { ft } , \mathrm { b } = 285.72 \mathrm { ft }$ 
B)  $\mathrm { B } = 74 ^ { \circ } 41 ^ { \prime } , \mathrm { a } = 77.36 \mathrm { ft } , \mathrm { b } = 283.63 \mathrm { ft }$ 
C)  $B = 74 ^ { \circ } 41 ^ { \prime } , \mathrm { a } = 77.93 \mathrm { ft } , \mathrm { b } = 284.52 \mathrm { ft }$ 
D)  $B = 75 ^ { \circ } 40 ^ { \prime } , \mathrm { a } = 77.93 \mathrm { ft } , \mathrm { b } = 280.52 \mathrm { ft }$

Question 11

Provide an appropriate response.
-Find the supplement of an angle whose measure is 89°.

Accepted Answer

A)  $91 ^ { \circ }$ 
B)  $1 ^ { \circ }$ 
C)  $269 ^ { \circ }$ 
D)  $179 ^ { \circ }$ 
A)  $91 ^ { \circ }$ 
B)  $1 ^ { \circ }$ 
C)  $269 ^ { \circ }$ 
D)  $179 ^ { \circ }$

Question 12

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$167 ^ { \circ } 2 ^ { \prime } 37 ^ { \prime \prime }$

Accepted Answer

A)  $167.05 ^ { \circ }$ 
B)  $167.04 ^ { \circ }$ 
C)  $167.10 ^ { \circ }$ 
D)  $167.00 ^ { \circ }$ 
A)  $167.05 ^ { \circ }$ 
B)  $167.04 ^ { \circ }$ 
C)  $167.10 ^ { \circ }$ 
D)  $167.00 ^ { \circ }$

Question 13

Convert the angle to degrees, minutes, and seconds.
-$82.72 ^ { \circ }$

Accepted Answer

A)  $82 ^ { \circ } 43 ^ { \prime } 72 ^ { \prime \prime }$ 
B)  $82 ^ { \circ } 43 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $82 ^ { \circ } 43 ^ { \prime } 18 ^ { \prime \prime }$ 
D)  $82 ^ { \circ } 43 ^ { \prime } 0 ^ { \prime \prime }$ 
A)  $82 ^ { \circ } 43 ^ { \prime } 72 ^ { \prime \prime }$ 
B)  $82 ^ { \circ } 43 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $82 ^ { \circ } 43 ^ { \prime } 18 ^ { \prime \prime }$ 
D)  $82 ^ { \circ } 43 ^ { \prime } 0 ^ { \prime \prime }$

Question 14

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
-$( 3,4 )$; Find $\sin \theta$.

Accepted Answer

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

Question 15

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
-$( 12,16 )$; Find $\cos \theta$.

Accepted Answer

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

Question 16

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
-Find $\sec B$ when $a = 9$ and $b = 5$.

Accepted Answer

A)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
B)  $\frac { \sqrt { 106 } } { 9 }$ 
C)  $\frac { 9 \sqrt { 106 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 106 } } { 106 }$ 
A)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
B)  $\frac { \sqrt { 106 } } { 9 }$ 
C)  $\frac { 9 \sqrt { 106 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 106 } } { 106 }$

Question 17

Solve the problem.
-The length of the base of an isosceles triangle is $13.02$ meters. Each base angle is $28.04 ^ { \circ }$. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Accepted Answer

A)  $7.38 \mathrm {~m}$ 
B)  $12.22 \mathrm {~m}$ 
C)  $13.85 \mathrm {~m}$ 
D)  $14.75 \mathrm {~m}$ 
A)  $7.38 \mathrm {~m}$ 
B)  $12.22 \mathrm {~m}$ 
C)  $13.85 \mathrm {~m}$ 
D)  $14.75 \mathrm {~m}$

Question 18

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $I$ and the positive $x$-axis is $\frac { \sqrt { 3 } } { 2 }$.

Accepted Answer

A)  $y = \frac { \sqrt { 3 } } { 2 } x$ 
B)  $y = \sqrt { 3 } x$ 
C)  $y = \frac { \sqrt { 3 } } { 3 } x$ 
D)  $y = x$ 
A)  $y = \frac { \sqrt { 3 } } { 2 } x$ 
B)  $y = \sqrt { 3 } x$ 
C)  $y = \frac { \sqrt { 3 } } { 3 } x$ 
D)  $y = x$

Question 19

The number represents an approximate measurement. State the range represented by the measurement.
-$12.6 \mathrm {~m}$

Accepted Answer

A)  $12.59 \mathrm {~m}$ to $12.61 \mathrm {~m}$ 
B)  $12.575 \mathrm {~m}$ to $12.625 \mathrm {~m}$ 
C)  $11.6 \mathrm {~m}$ to $13.6 \mathrm {~m}$ 
D)  $12.55 \mathrm {~m}$ to $12.65 \mathrm {~m}$ 
A)  $12.59 \mathrm {~m}$ to $12.61 \mathrm {~m}$ 
B)  $12.575 \mathrm {~m}$ to $12.625 \mathrm {~m}$ 
C)  $11.6 \mathrm {~m}$ to $13.6 \mathrm {~m}$ 
D)  $12.55 \mathrm {~m}$ to $12.65 \mathrm {~m}$

Question 20

Solve the problem.
-An airplane travels at $120 \mathrm {~km} / \mathrm { h }$ for $2 \mathrm { hr }$ in a direction of $120 ^ { \circ }$ from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?

Accepted Answer

A)  $120 \mathrm {~km}$ 
B)  $277 \mathrm {~km}$ 
C)  $208 \mathrm {~km}$ 
D)  $139 \mathrm {~km}$ 
A)  $120 \mathrm {~km}$ 
B)  $277 \mathrm {~km}$ 
C)  $208 \mathrm {~km}$ 
D)  $139 \mathrm {~km}$

Find the exact value of the expression. - $\csc \left( - 960 ^ { \circ } \right)$

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. - $\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

Find the measure of each angle in the problem. -

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\cos 205 ^ { \circ } 3 ^ { \prime }$

Solve the problem. -Find $\mathrm { h }$ as indicated in the figure. Round to the nearest meter. $Solve the problem. -Find \mathrm { h } as indicated in the figure. Round to the nearest meter.$

Find the exact value of the expression. - $\cos 2040 ^ { \circ }$

An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of θ. Do not use a calculator. - $- 7 x - 5 y = 0 , x \leq 0 ; \quad$ Find $\sec \theta$

Solve the right triangle. - $\mathrm { A } = 15 ^ { \circ } 19 ^ { \prime } , \mathrm { c } = 295 \mathrm { ft } , \mathrm { C } = 90 ^ { \circ }$ Round side lengths to two decimal places, if necessary.

Provide an appropriate response. -Find the supplement of an angle whose measure is 89°.

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $167 ^ { \circ } 2 ^ { \prime } 37 ^ { \prime \prime }$

Convert the angle to degrees, minutes, and seconds. - $82.72 ^ { \circ }$

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 3,4 )$ ; Find $\sin \theta$ .

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 12,16 )$ ; Find $\cos \theta$ .

Solve the problem. -The length of the base of an isosceles triangle is $13.02$ meters. Each base angle is $28.04 ^ { \circ }$ . Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

The number represents an approximate measurement. State the range represented by the measurement. - $12.6 \mathrm {~m}$

Solve the problem. -An airplane travels at $120 \mathrm {~km} / \mathrm { h }$ for $2 \mathrm { hr }$ in a direction of $120 ^ { \circ }$ from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 5: Trigonometric Functions

Find the exact value of the expression. - csc⁡(−960∘)\csc \left( - 960 ^ { \circ } \right)csc(−960∘)

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. - I,ry\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }I,yr​

Find the measure of each angle in the problem. -

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - cos⁡205∘3′\cos 205 ^ { \circ } 3 ^ { \prime }cos205∘3′

Solve the problem. -Find h\mathrm { h }h as indicated in the figure. Round to the nearest meter.

Find the exact value of the expression. - cos⁡2040∘\cos 2040 ^ { \circ }cos2040∘

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - B=74∘24′,b=11 km\mathrm { B } = 74 ^ { \circ } 24 ^ { \prime } , \mathrm { b } = 11 \mathrm {~km}B=74∘24′,b=11 km Round side lengths to one decimal place.

An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of θ. Do not use a calculator. - −7x−5y=0,x≤0;- 7 x - 5 y = 0 , x \leq 0 ; \quad−7x−5y=0,x≤0; Find sec⁡θ\sec \thetasecθ

Solve the right triangle. - A=15∘19′,c=295ft,C=90∘\mathrm { A } = 15 ^ { \circ } 19 ^ { \prime } , \mathrm { c } = 295 \mathrm { ft } , \mathrm { C } = 90 ^ { \circ }A=15∘19′,c=295ft,C=90∘ Round side lengths to two decimal places, if necessary.