Question 1

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, $\frac { y } { x }$

Accepted Answer

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

Question 2

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
-$\sin \theta = - \frac { \sqrt { 2 } } { 2 }$

Accepted Answer

A)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
A)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
C)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
D)  $45 ^ { \circ }$ and $225 ^ { \circ }$ C

Question 3

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-$\cos 67.8 ^ { \circ }$

Accepted Answer

A)  $\sin 22.2 ^ { \circ }$ 
B)  $\cos 112.2 ^ { \circ }$ 
C)  $\sec 112.2 ^ { \circ }$ 
D)  $\sin 67.8 ^ { \circ }$ 
A)  $\sin 22.2 ^ { \circ }$ 
B)  $\cos 112.2 ^ { \circ }$ 
C)  $\sec 112.2 ^ { \circ }$ 
D)  $\sin 67.8 ^ { \circ }$ A

Question 4

Find the exact value of the expression.
-$\cot 45 ^ { \circ }$

Accepted Answer

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

Question 5

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\sec 30 ^ { \circ }$

Accepted Answer

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

Question 6

Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \frac { 5 } { 4 }$ and $\cos \theta < 0$.

Accepted Answer

A)  $- \frac { 5 \sqrt { 41 } } { 41 }$ 
B)  $- \frac { \sqrt { 41 } } { 5 }$ 
C)  $\frac { 5 \sqrt { 41 } } { 41 }$ 
D)  $\frac { \sqrt { 41 } } { 4 }$ 
A)  $- \frac { 5 \sqrt { 41 } } { 41 }$ 
B)  $- \frac { \sqrt { 41 } } { 5 }$ 
C)  $\frac { 5 \sqrt { 41 } } { 41 }$ 
D)  $\frac { \sqrt { 41 } } { 4 }$

Question 7

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-sec θ = 2.500967

Accepted Answer

A)  48.2226925° 
B)  66.4314897° 
C)  23.5685103° 
D)  21.7937700° 
A)  48.2226925° 
B)  66.4314897° 
C)  23.5685103° 
D)  21.7937700°

Question 8

Decide whether the statement is possible or impossible for an angle θ.
-$\sin \theta = 0.6$ and $\csc \theta = - 0.6$

Accepted Answer

A)  Possible 
B)  Impossible 
A)  Possible 
B)  Impossible

Question 9

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.
-$\mathrm { IV } , \frac { \mathrm { r } } { \mathrm { y } }$

Accepted Answer

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

Question 10

Identify the quadrant for the angle θ satisfying the following conditions.
-$\tan \theta > 0$ and $\sin \theta < 0$

Accepted Answer

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

Question 11

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\frac { \sin 14 ^ { \circ } } { \cos 14 ^ { \circ } }$

Accepted Answer

A)  1 
B)  $4.0107809$ 
C)  $0.249328$ 
D)  $0.0174551$ 
A)  1 
B)  $4.0107809$ 
C)  $0.249328$ 
D)  $0.0174551$

Question 12

Find the angle of least positive measure coterminal with the given angle.
-$1378 ^ { \circ }$

Accepted Answer

A)  $118 ^ { \circ }$ 
B)  $208 ^ { \circ }$ 
C)  $658 ^ { \circ }$ 
D)  $298 ^ { \circ }$ 
A)  $118 ^ { \circ }$ 
B)  $208 ^ { \circ }$ 
C)  $658 ^ { \circ }$ 
D)  $298 ^ { \circ }$

Question 13

Solve the problem.
-Find the exact value of $x$ in the figure.

Accepted Answer

A)  $39 \sqrt { 6 }$ 
B)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 10 \sqrt { 6 } } { 3 }$ 
D)  $\frac { 40 \sqrt { 6 } } { 3 }$ 
A)  $39 \sqrt { 6 }$ 
B)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 10 \sqrt { 6 } } { 3 }$ 
D)  $\frac { 40 \sqrt { 6 } } { 3 }$

Question 14

Solve the problem.
-The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin θ, where W is the weight of the car and θ is the angle of the hillʹs grade (θ > 0 for uphill travel, θ < 0
For downhill travel). Find the weight of the car (to the nearest pound) that is traveling on a -2.1°
Downhill grade and which has a grade resistance of -95.27 lb.

Accepted Answer

A)  2900 lb 
B)  2400 lb 
C)  2700 lb 
D)  2600 lb 
A)  2900 lb 
B)  2400 lb 
C)  2700 lb 
D)  2600 lb

Question 15

Solve the problem.
-An airplane travels at $105 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $321 ^ { \circ }$ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

Accepted Answer

A)  $330 \mathrm {~km}$ 
B)  $648 \mathrm {~km}$ 
C)  $408 \mathrm {~km}$ 
D)  $834 \mathrm {~km}$ 
A)  $330 \mathrm {~km}$ 
B)  $648 \mathrm {~km}$ 
C)  $408 \mathrm {~km}$ 
D)  $834 \mathrm {~km}$

Question 16

Solve the problem.
-Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that cuts off the same arc. See the figure.)

Accepted Answer

A)  $90 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $75 ^ { \circ }$ 
D)  $45 ^ { \circ }$ 
A)  $90 ^ { \circ }$ 
B)  $60 ^ { \circ }$ 
C)  $75 ^ { \circ }$ 
D)  $45 ^ { \circ }$

Question 17

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an
airplane located at that point. Express the bearing using both methods.
-$( 2,0 )$

Accepted Answer

A)  $90 ^ { \circ } ; \mathrm { N } \mathrm {} 90 ^ { \circ } \mathrm { E }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { E }$ 
B)  $270 ^ { \circ } ; \mathrm { N } 90 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { W }$ 
C)  $270 ^ { \circ } ; \mathrm { N } \mathrm {} 90 ^ { \circ } \mathrm { E }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { E }$ 
D)  $90 ^ { \circ } ; \mathrm { N } 90 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { W }$ 
A)  $90 ^ { \circ } ; \mathrm { N } \mathrm {} 90 ^ { \circ } \mathrm { E }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { E }$ 
B)  $270 ^ { \circ } ; \mathrm { N } 90 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { W }$ 
C)  $270 ^ { \circ } ; \mathrm { N } \mathrm {} 90 ^ { \circ } \mathrm { E }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { E }$ 
D)  $90 ^ { \circ } ; \mathrm { N } 90 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 90 ^ { \circ } \mathrm { W }$

Question 18

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $40 ^ { \circ }$ and $50 ^ { \circ }$ 
B)  $20 ^ { \circ }$ and $30 ^ { \circ }$ 
C)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
D)  $20 ^ { \circ }$ and $25 ^ { \circ }$ 
A)  $40 ^ { \circ }$ and $50 ^ { \circ }$ 
B)  $20 ^ { \circ }$ and $30 ^ { \circ }$ 
C)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
D)  $20 ^ { \circ }$ and $25 ^ { \circ }$

Question 19

The number represents an approximate measurement. State the range represented by the measurement.
-$22 \mathrm { ft }$

Accepted Answer

A)  $21.75 \mathrm { ft }$ to $22.25 \mathrm { ft }$ 
B)  $21 \mathrm { ft }$ to $23 \mathrm { ft }$ 
C)  $21.9 \mathrm { ft }$ to $22.1 \mathrm { ft }$ 
D)  $21.5 \mathrm { ft }$ to $22.5 \mathrm { ft }$ 
A)  $21.75 \mathrm { ft }$ to $22.25 \mathrm { ft }$ 
B)  $21 \mathrm { ft }$ to $23 \mathrm { ft }$ 
C)  $21.9 \mathrm { ft }$ to $22.1 \mathrm { ft }$ 
D)  $21.5 \mathrm { ft }$ to $22.5 \mathrm { ft }$

Question 20

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 $\cos \mathrm { A }$ when $\mathrm { a } = 3$ and $\mathrm { b } = 8$.

Accepted Answer

A)  $\frac { \sqrt { 73 } } { 3 }$ 
B)  $\frac { 8 \sqrt { 73 } } { 73 }$ 
C)  $\frac { \sqrt { 73 } } { 8 }$ 
D)  $\frac { 3 \sqrt { 73 } } { 73 }$ 
A)  $\frac { \sqrt { 73 } } { 3 }$ 
B)  $\frac { 8 \sqrt { 73 } } { 73 }$ 
C)  $\frac { \sqrt { 73 } } { 8 }$ 
D)  $\frac { 3 \sqrt { 73 } } { 73 }$

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, $\frac { y } { x }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { \sqrt { 2 } } { 2 }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\cos 67.8 ^ { \circ }$

Find the exact value of the expression. - $\cot 45 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sec 30 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\cot \theta = - \frac { 5 } { 4 }$ and $\cos \theta < 0$ .

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -sec θ = 2.500967

Decide whether the statement is possible or impossible for an angle θ. - $\sin \theta = 0.6$ and $\csc \theta = - 0.6$

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. - $\mathrm { IV } , \frac { \mathrm { r } } { \mathrm { y } }$

Identify the quadrant for the angle θ satisfying the following conditions. - $\tan \theta > 0$ and $\sin \theta < 0$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\frac { \sin 14 ^ { \circ } } { \cos 14 ^ { \circ } }$

Find the angle of least positive measure coterminal with the given angle. - $1378 ^ { \circ }$

Solve the problem. -Find the exact value of $x$ in the figure.

Solve the problem. -An airplane travels at $105 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $321 ^ { \circ }$ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. - $( 2,0 )$

Find the measure of each angle in the problem. -

The number represents an approximate measurement. State the range represented by the measurement. - $22 \mathrm { ft }$

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

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\frac { y } { x }xy​

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - sin⁡θ=−22\sin \theta = - \frac { \sqrt { 2 } } { 2 }sinθ=−22​​

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - cos⁡67.8∘\cos 67.8 ^ { \circ }cos67.8∘

Find the exact value of the expression. - cot⁡45∘\cot 45 ^ { \circ }cot45∘

Without using a calculator, give the exact trigonometric function value with rational denominator. - sec⁡30∘\sec 30 ^ { \circ }sec30∘

Use the fundamental identities to find the value of the trigonometric function. -Find csc⁡θ\csc \thetacscθ , given that cot⁡θ=−54\cot \theta = - \frac { 5 } { 4 }cotθ=−45​ and cos⁡θ<0\cos \theta < 0cosθ<0 .