Question 1

Find the angle of least positive measure coterminal with the given angle.
-$- 44 ^ { \circ }$

Accepted Answer

A)  $226 ^ { \circ }$ 
B)  $44 ^ { \circ }$ 
C)  $46 ^ { \circ }$ 
D)  $316 ^ { \circ }$ 
A)  $226 ^ { \circ }$ 
B)  $44 ^ { \circ }$ 
C)  $46 ^ { \circ }$ 
D)  $316 ^ { \circ }$

Question 2

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$219 ^ { \circ } 12 ^ { \prime } 24 ^ { \prime \prime }$

Accepted Answer

A)  $219.22 ^ { \circ }$ 
B)  $219.17 ^ { \circ }$ 
C)  $219.21 ^ { \circ }$ 
D)  $219.27 ^ { \circ }$ 
A)  $219.22 ^ { \circ }$ 
B)  $219.17 ^ { \circ }$ 
C)  $219.21 ^ { \circ }$ 
D)  $219.27 ^ { \circ }$

Question 3

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 $\tan B$ when $b = 6$ and $c = 7$.

Accepted Answer

A)  $\frac { 7 \sqrt { 13 } } { 13 }$ 
B)  $\frac { \sqrt { 13 } } { 7 }$ 
C)  $\frac { 6 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 6 }$ 
A)  $\frac { 7 \sqrt { 13 } } { 13 }$ 
B)  $\frac { \sqrt { 13 } } { 7 }$ 
C)  $\frac { 6 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 6 }$

Question 4

Solve the problem.
-A $5.8$ - $\mathrm { ft }$ fence is $15.431 \mathrm { ft }$ away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find $\theta$, the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree when necessary.

Accepted Answer

A)  $\theta = 22 ^ { \circ }$ 
B)  $\theta = 20.4 ^ { \circ }$ 
C)  $\theta = 20.8 ^ { \circ }$ 
D)  $\theta = 20.6 ^ { \circ }$ 
A)  $\theta = 22 ^ { \circ }$ 
B)  $\theta = 20.4 ^ { \circ }$ 
C)  $\theta = 20.8 ^ { \circ }$ 
D)  $\theta = 20.6 ^ { \circ }$

Question 5

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal
side of $\theta$ (3, 6) 
-$( - 2,5 )$

Accepted Answer

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

Question 6

Identify the quadrant for the angle $\theta$ satisfying the following conditions.
-$\cos \theta < 0 \text { and } \csc \theta < 0$

Accepted Answer

A)  Quadrant II 
B)  Quadrant III 
C)  Quadrant I 
D)  Quadrant IV 
A)  Quadrant II 
B)  Quadrant III 
C)  Quadrant I 
D)  Quadrant IV

Question 7

Evaluate the expression.
-$\csc 450 ^ { \circ }$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  Undefined 
A)  1 
B)  2 
C)  0 
D)  Undefined

Question 8

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\cot 45 ^ { \circ }$

Accepted Answer

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

Question 9

Solve the problem.
-A ship travels $74 \mathrm {~km}$ on a bearing of $38 ^ { \circ }$, and then travels on a bearing of $128 ^ { \circ }$ for $122 \mathrm {~km}$. Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Accepted Answer

A)  $143 \mathrm {~km}$ 
B)  $196 \mathrm {~km}$ 
C)  $58 \mathrm {~km}$ 
D)  $46 \mathrm {~km}$ 
A)  $143 \mathrm {~km}$ 
B)  $196 \mathrm {~km}$ 
C)  $58 \mathrm {~km}$ 
D)  $46 \mathrm {~km}$

Question 10

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.
-$\text { II, } \frac { y } { x }$

Accepted Answer

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

Question 11

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.
-$\text { III, } \frac { x } { r }$

Accepted Answer

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

Question 12

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$\csc \theta$, given that $\sin \theta = - 0.2817$

Accepted Answer

A)  $- 3.550$ 
B)  $3.550$ 
C)  $1.775$ 
D)  $- 1.775$ 
A)  $- 3.550$ 
B)  $3.550$ 
C)  $1.775$ 
D)  $- 1.775$

Question 13

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$, where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). Find the weight of the car (to the nearest pound) that is traveling on a $- 2.6 ^ { \circ }$ downhill grade and which has a grade resistance of $- 140.63 \mathrm { lb }$.

Accepted Answer

A)  $2900 \mathrm { lb }$ 
B)  $3200 \mathrm { lb }$ 
C)  $3100 \mathrm { lb }$ 
D)  $3400 \mathrm { lb }$ 
A)  $2900 \mathrm { lb }$ 
B)  $3200 \mathrm { lb }$ 
C)  $3100 \mathrm { lb }$ 
D)  $3400 \mathrm { lb }$

Question 14

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
C)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $135 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
C)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $135 ^ { \circ }$

Question 15

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-$- 21 ^ { \circ }$

Accepted Answer

A)  $- 21 ^ { \circ } + n \cdot 180 ^ { \circ }$ 
B)  $- 21 ^ { \circ } - n \cdot 180 ^ { \circ }$ 
C)  $- 21 ^ { \circ } + n \cdot 360 ^ { \circ }$ 
D)  $- 21 ^ { \circ } + 2 n \cdot 360 ^ { \circ }$ 
A)  $- 21 ^ { \circ } + n \cdot 180 ^ { \circ }$ 
B)  $- 21 ^ { \circ } - n \cdot 180 ^ { \circ }$ 
C)  $- 21 ^ { \circ } + n \cdot 360 ^ { \circ }$ 
D)  $- 21 ^ { \circ } + 2 n \cdot 360 ^ { \circ }$

Question 16

Evaluate the expression.
-$$\sin ^ { 2 } 360 ^ { \circ } + \cos ^ { 2 } 360 ^ { \circ }$$

Accepted Answer

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

Question 17

Convert the angle to degrees, minutes, and seconds.
-$332.68 ^ { \circ }$

Accepted Answer

A)  $332 ^ { \circ } 40 ^ { \prime } 68 ^ { \prime \prime }$ 
B)  $332 ^ { \circ } 47 ^ { \prime } 68 ^ { \prime \prime }$ 
C)  $332 ^ { \circ } 41 ^ { \prime } 47 ^ { \prime \prime }$ 
D)  $332 ^ { \circ } 40 ^ { \prime } 48 ^ { \prime \prime }$ 
A)  $332 ^ { \circ } 40 ^ { \prime } 68 ^ { \prime \prime }$ 
B)  $332 ^ { \circ } 47 ^ { \prime } 68 ^ { \prime \prime }$ 
C)  $332 ^ { \circ } 41 ^ { \prime } 47 ^ { \prime \prime }$ 
D)  $332 ^ { \circ } 40 ^ { \prime } 48 ^ { \prime \prime }$

Question 18

Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $- 4$ 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $- 4$

Question 19

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-$$\mathrm { a } = 3.9 \mathrm {~cm} , \mathrm {~b} = 1.2 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 17.9 ^ { \circ } , \mathrm { B } = 72.1 ^ { \circ } , \mathrm { c } = 5.1 \mathrm {~cm}$ 
B)  $\mathrm { A } = 72.9 ^ { \circ } , \mathrm { B } = 17.1 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$ 
C)  $\mathrm { A } = 68.4 ^ { \circ } , \mathrm { B } = 21.6 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$ 
D)  $\mathrm { A } = 17.1 ^ { \circ } , \mathrm { B } = 72.9 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$ 
A)  $\mathrm { A } = 17.9 ^ { \circ } , \mathrm { B } = 72.1 ^ { \circ } , \mathrm { c } = 5.1 \mathrm {~cm}$ 
B)  $\mathrm { A } = 72.9 ^ { \circ } , \mathrm { B } = 17.1 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$ 
C)  $\mathrm { A } = 68.4 ^ { \circ } , \mathrm { B } = 21.6 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$ 
D)  $\mathrm { A } = 17.1 ^ { \circ } , \mathrm { B } = 72.9 ^ { \circ } , \mathrm { c } = 4.1 \mathrm {~cm}$

Question 20

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-A 37 -foot ladder is leaning against the side of a building. If the ladder makes an angle of $29 ^ { \circ } 20 ^ { \prime }$ with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place when necessary.

Accepted Answer

A)  $18.13 \mathrm { ft }$ 
B)  $8.76 \mathrm { ft }$ 
C)  $19.43 \mathrm { ft }$ 
D)  $23.83 \mathrm { ft }$ 
A)  $18.13 \mathrm { ft }$ 
B)  $8.76 \mathrm { ft }$ 
C)  $19.43 \mathrm { ft }$ 
D)  $23.83 \mathrm { ft }$

Find the angle of least positive measure coterminal with the given angle. - $- 44 ^ { \circ }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $219 ^ { \circ } 12 ^ { \prime } 24 ^ { \prime \prime }$

Identify the quadrant for the angle $\theta$ satisfying the following conditions. - $\cos \theta < 0 \text { and } \csc \theta < 0$

Evaluate the expression. - $\csc 450 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cot 45 ^ { \circ }$

Solve the problem. -A ship travels $74 \mathrm {~km}$ on a bearing of $38 ^ { \circ }$ , and then travels on a bearing of $128 ^ { \circ }$ for $122 \mathrm {~km}$ . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

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. - $\text { II, } \frac { y } { x }$

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. - $\text { III, } \frac { x } { r }$

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\csc \theta$ , given that $\sin \theta = - 0.2817$

Find the measure of each angle in the problem. -

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 21 ^ { \circ }$

Evaluate the expression. - $\sin ^ { 2 } 360 ^ { \circ } + \cos ^ { 2 } 360 ^ { \circ }$

Convert the angle to degrees, minutes, and seconds. - $332.68 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\cot \theta = - \sqrt { 15 }$ and $\theta$ is in quadrant II.

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { a } = 3.9 \mathrm {~cm} , \mathrm {~b} = 1.2 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Review of Basic Concepts

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

Filters

Exam 6: Trigonometric Functions

Find the angle of least positive measure coterminal with the given angle. - −44∘- 44 ^ { \circ }−44∘

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 219∘12′24′′219 ^ { \circ } 12 ^ { \prime } 24 ^ { \prime \prime }219∘12′24′′

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point is on the terminal side of θ\thetaθ (3, 6) - (−2,5)( - 2,5 )(−2,5)

Identify the quadrant for the angle θ\thetaθ satisfying the following conditions. - cos⁡θ<0 and csc⁡θ<0\cos \theta < 0 \text { and } \csc \theta < 0cosθ<0 and cscθ<0

Evaluate the expression. - csc⁡450∘\csc 450 ^ { \circ }csc450∘

Without using a calculator, give the exact trigonometric function value with rational denominator. - cot⁡45∘\cot 45 ^ { \circ }cot45∘

Solve the problem. -A ship travels 74 km74 \mathrm {~km}74 km on a bearing of 38∘38 ^ { \circ }38∘ , and then travels on a bearing of 128∘128 ^ { \circ }128∘ for 122 km122 \mathrm {~km}122 km . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

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. - II, yx\text { II, } \frac { y } { x } II, xy​

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. - III, xr\text { III, } \frac { x } { r } III, rx​

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - csc⁡θ\csc \thetacscθ , given that sin⁡θ=−0.2817\sin \theta = - 0.2817sinθ=−0.2817