Question 1

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-$\tan \theta = 2.0525017$

Accepted Answer

A)  $115.975821 ^ { \circ }$ 
B)  $64.0241786 ^ { \circ }$ 
C)  $244.024179 ^ { \circ }$ 
D)  $25.9758214 ^ { \circ }$ 
A)  $115.975821 ^ { \circ }$ 
B)  $64.0241786 ^ { \circ }$ 
C)  $244.024179 ^ { \circ }$ 
D)  $25.9758214 ^ { \circ }$

Question 2

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { a } = 17.2 \mathrm {~cm} , \mathrm {~b} = 25.7 \mathrm {~cm}$$
Round the missing side length to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 42 ^ { \circ } 1 ^ { \prime } ; \mathrm { B } = 47 ^ { \circ } 59 ^ { \prime } ; \mathrm { c } = 30.9 \mathrm {~cm}$ 
B)  $\mathrm { A } = 33 ^ { \circ } 48 ^ { \prime } ; \mathrm { B } = 56 ^ { \circ } 12 ^ { \prime } ; \mathrm { c } = 32.8 \mathrm {~cm}$ 
C)  $A = 42 ^ { \circ } 1 ^ { \prime } ; B = 47 ^ { \circ } 59 ^ { \prime } ; \mathrm { c } = 28.7 \mathrm {~cm}$ 
D)  $\mathrm { A } = 33 ^ { \circ } 48 ^ { \prime } ; \mathrm { B } = 56 ^ { \circ } 12 ^ { \prime } ; \mathrm { c } = 30.9 \mathrm {~cm}$ 
A)  $\mathrm { A } = 42 ^ { \circ } 1 ^ { \prime } ; \mathrm { B } = 47 ^ { \circ } 59 ^ { \prime } ; \mathrm { c } = 30.9 \mathrm {~cm}$ 
B)  $\mathrm { A } = 33 ^ { \circ } 48 ^ { \prime } ; \mathrm { B } = 56 ^ { \circ } 12 ^ { \prime } ; \mathrm { c } = 32.8 \mathrm {~cm}$ 
C)  $A = 42 ^ { \circ } 1 ^ { \prime } ; B = 47 ^ { \circ } 59 ^ { \prime } ; \mathrm { c } = 28.7 \mathrm {~cm}$ 
D)  $\mathrm { A } = 33 ^ { \circ } 48 ^ { \prime } ; \mathrm { B } = 56 ^ { \circ } 12 ^ { \prime } ; \mathrm { c } = 30.9 \mathrm {~cm}$

Question 3

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
-$\csc \left( - 122 ^ { \circ } \right)$ and $\cot \left( - 122 ^ { \circ } \right)$

Accepted Answer

A)  positive and positive 
B)  positive and negative 
C)  negative and negative 
D)  negative and positive 
A)  positive and positive 
B)  positive and negative 
C)  negative and negative 
D)  negative and positive

Question 4

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.
-$- 7 x - 5 y = 0 , x \geq 0 ; \quad$ Find $\cos \theta$

Accepted Answer

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

Question 5

Convert the angle to degrees, minutes, and seconds.
-$355.52 ^ { \circ }$

Accepted Answer

A)  $355 ^ { \circ } 31 ^ { \prime } 52 ^ { \prime \prime }$ 
B)  $355 ^ { \circ } 32 ^ { \prime } 11 ^ { \prime \prime }$ 
C)  $355 ^ { \circ } 31 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $355 ^ { \circ } 11 ^ { \prime } 52 ^ { \prime \prime }$ 
A)  $355 ^ { \circ } 31 ^ { \prime } 52 ^ { \prime \prime }$ 
B)  $355 ^ { \circ } 32 ^ { \prime } 11 ^ { \prime \prime }$ 
C)  $355 ^ { \circ } 31 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $355 ^ { \circ } 11 ^ { \prime } 52 ^ { \prime \prime }$

Question 6

Solve the problem.
-Any offset between a stationary radar gun and a moving target creates a ʺcosine effectʺ that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That
Is, the radar speed reading is the product of the actual reading and the cosine of the angle. Find the
Radar reading to the nearest hundredth for the auto shown in the figure.

Accepted Answer

A)  $89.83 \mathrm { mph }$ 
B)  $93.97 \mathrm { mph }$ 
C)  $24.07 \mathrm { mph }$ 
D)  $92.03 \mathrm { mph }$ 
A)  $89.83 \mathrm { mph }$ 
B)  $93.97 \mathrm { mph }$ 
C)  $24.07 \mathrm { mph }$ 
D)  $92.03 \mathrm { mph }$

Question 7

Solve the problem.
-A formula used by an engineer to determine the safe radius of a curve, $R$, when designing a road is:
$\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$, where $\alpha$ is the superelevation of the road and $\mathrm { V }$ is the velocity (in feet per second) for which the curve is designed. If $\mathrm { V } = 81 \mathrm { ft }$ per sec, $\mathrm { f } = 0.1 , \mathrm {~g} = 30$, and $\alpha = 1.1 ^ { \circ }$, find $\mathrm { R }$. Round to the nearest foot.

Accepted Answer

A)  $R = 1832 \mathrm { ft }$ 
B)  $R = 1845 \mathrm { ft }$ 
C)  $R = 1838 \mathrm { ft }$ 
D)  $\mathrm { R } = 1835 \mathrm { ft }$ 
A)  $R = 1832 \mathrm { ft }$ 
B)  $R = 1845 \mathrm { ft }$ 
C)  $R = 1838 \mathrm { ft }$ 
D)  $\mathrm { R } = 1835 \mathrm { ft }$

Question 8

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, $\frac { \mathrm { r } } { \mathrm { x } }$

Accepted Answer

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

Question 9

Solve the problem.
-From a boat on the river below a dam, the angle of elevation to the top of the dam is $13 ^ { \circ } 58 ^ { \prime }$. If the dam is 1732 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Accepted Answer

A)  $6964 \mathrm { ft }$ 
B)  $6944 \mathrm { ft }$ 
C)  $6954 \mathrm { ft }$ 
D)  $6934 \mathrm { ft }$ 
A)  $6964 \mathrm { ft }$ 
B)  $6944 \mathrm { ft }$ 
C)  $6954 \mathrm { ft }$ 
D)  $6934 \mathrm { ft }$

Question 10

Use the fundamental identities to find the value of the trigonometric function.
-Find $\tan \theta$, given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $- \frac { \sqrt { 7 } } { 9 }$ 
B)  $- \frac { 3 \sqrt { 7 } } { 7 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  $- \frac { \sqrt { 7 } } { 9 }$ 
B)  $- \frac { 3 \sqrt { 7 } } { 7 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 5 } { 4 }$

Question 11

Evaluate the function requested. Write your answer as a fraction in lowest terms.
- 
Find $\cos B$.

Accepted Answer

A)  $\cos B = \frac { 40 } { 41 }$ 
B)  $\cos B = \frac { 9 } { 41 }$ 
C)  $\cos B = \frac { 9 } { 40 }$ 
D)  $\cos \mathrm { B } = \frac { 41 } { 40 }$ 
A)  $\cos B = \frac { 40 } { 41 }$ 
B)  $\cos B = \frac { 9 } { 41 }$ 
C)  $\cos B = \frac { 9 } { 40 }$ 
D)  $\cos \mathrm { B } = \frac { 41 } { 40 }$

Question 12

Provide an appropriate response.
-Find the complement of an angle whose measure is $38 ^ { \circ }$.

Accepted Answer

A)  $38 ^ { \circ }$ 
B)  $142 ^ { \circ }$ 
C)  $52 ^ { \circ }$ 
D)  $128 ^ { \circ }$ 
A)  $38 ^ { \circ }$ 
B)  $142 ^ { \circ }$ 
C)  $52 ^ { \circ }$ 
D)  $128 ^ { \circ }$

Question 13

Solve the problem for the given information.
-Find the equation of a line passing through the origin and making a $$45 ^ { \circ }$$ angle with the positive x-axis.

Accepted Answer

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

Question 14

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $15 ^ { \circ }$ and $30 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
C)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
D)  $17 ^ { \circ }$ and $34 ^ { \circ }$ 
A)  $15 ^ { \circ }$ and $30 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
C)  $30 ^ { \circ }$ and $60 ^ { \circ }$ 
D)  $17 ^ { \circ }$ and $34 ^ { \circ }$

Question 15

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { A } = 16 ^ { \circ } 41 ^ { \prime } , \mathrm { c } = 299 \mathrm { ft }$$
Round side lengths to two decimal places.

Accepted Answer

A)  $B = 73 ^ { \circ } 19 ^ { \prime } ; a = 85.84 \mathrm { ft } ; b = 286.41 \mathrm { ft }$ 
B)  $\mathrm { B } = 74 ^ { \circ } 18 ^ { \prime } ; \mathrm { a } = 85.84 \mathrm { ft } ; \mathrm { b } = 282.41 \mathrm { ft }$ 
C)  $\mathrm { B } = 73 ^ { \circ } 18 ^ { \prime } ; \mathrm { a } = 89.04 \mathrm { ft } ; \mathrm { b } = 287.61 \mathrm { ft }$ 
D)  $B = 73 ^ { \circ } 19 ^ { \prime } ; \mathrm { a } = 85.27 \mathrm { ft } ; \mathrm { b } = 285.52 \mathrm { ft }$ 
A)  $B = 73 ^ { \circ } 19 ^ { \prime } ; a = 85.84 \mathrm { ft } ; b = 286.41 \mathrm { ft }$ 
B)  $\mathrm { B } = 74 ^ { \circ } 18 ^ { \prime } ; \mathrm { a } = 85.84 \mathrm { ft } ; \mathrm { b } = 282.41 \mathrm { ft }$ 
C)  $\mathrm { B } = 73 ^ { \circ } 18 ^ { \prime } ; \mathrm { a } = 89.04 \mathrm { ft } ; \mathrm { b } = 287.61 \mathrm { ft }$ 
D)  $B = 73 ^ { \circ } 19 ^ { \prime } ; \mathrm { a } = 85.27 \mathrm { ft } ; \mathrm { b } = 285.52 \mathrm { ft }$

Question 16

Solve the problem.
-From the top of a vertical tower, 362 feet above the the surface of the earth, the angle of depression to a doghouse is $27 ^ { \circ } 20 ^ { \prime }$. How far is it from the doghouse to the foot of the tower? Round your answer to the hundredths place when necessary.

Accepted Answer

A)  $802.96 \mathrm { ft }$ 
B)  $712.76 \mathrm { ft }$ 
C)  $700.36 \mathrm { ft }$ 
D)  $684.77 \mathrm { ft }$ 
A)  $802.96 \mathrm { ft }$ 
B)  $712.76 \mathrm { ft }$ 
C)  $700.36 \mathrm { ft }$ 
D)  $684.77 \mathrm { ft }$

Question 17

Perform the calculation.
-$79 ^ { \circ } 58 ^ { \prime } + 322 ^ { \circ } 33 ^ { \prime }$

Accepted Answer

A)  $402 ^ { \circ } 91 ^ { \prime }$ 
B)  $32 ^ { \circ } 31 ^ { \prime }$ 
C)  $402 ^ { \circ } 31 ^ { \prime }$ 
D)  $32 ^ { \circ } 91 ^ { \prime }$ 
A)  $402 ^ { \circ } 91 ^ { \prime }$ 
B)  $32 ^ { \circ } 31 ^ { \prime }$ 
C)  $402 ^ { \circ } 31 ^ { \prime }$ 
D)  $32 ^ { \circ } 91 ^ { \prime }$

Question 18

Perform the calculation.
-$90 ^ { \circ } - 38 ^ { \circ } 21 ^ { \prime }$

Accepted Answer

A)  $52 ^ { \circ } 39 ^ { \prime }$ 
B)  $51 ^ { \circ } 21 ^ { \prime }$ 
C)  $51 ^ { \circ } 39 ^ { \prime }$ 
D)  $52 ^ { \circ } 21 ^ { \prime }$ 
A)  $52 ^ { \circ } 39 ^ { \prime }$ 
B)  $51 ^ { \circ } 21 ^ { \prime }$ 
C)  $51 ^ { \circ } 39 ^ { \prime }$ 
D)  $52 ^ { \circ } 21 ^ { \prime }$

Question 19

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
-$$\sin \theta = \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
C)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
A)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
C)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$

Question 20

Solve the problem.
-Find a formula for the area of the figure in terms of s.

Accepted Answer

A)  $\sqrt { 6 } \mathrm {~s} ^ { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 6 } s ^ { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$ 
D)  $\frac { \sqrt { 6 } } { 4 } \mathrm {~s} ^ { 2 }$ 
A)  $\sqrt { 6 } \mathrm {~s} ^ { 2 }$ 
B)  $\frac { \sqrt { 3 } } { 6 } s ^ { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$ 
D)  $\frac { \sqrt { 6 } } { 4 } \mathrm {~s} ^ { 2 }$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\tan \theta = 2.0525017$

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - $\csc \left( - 122 ^ { \circ } \right)$ and $\cot \left( - 122 ^ { \circ } \right)$

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. - $- 7 x - 5 y = 0 , x \geq 0 ; \quad$ Find $\cos \theta$

Convert the angle to degrees, minutes, and seconds. - $355.52 ^ { \circ }$

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, $\frac { \mathrm { r } } { \mathrm { x } }$

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $13 ^ { \circ } 58 ^ { \prime }$ . If the dam is 1732 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Use the fundamental identities to find the value of the trigonometric function. -Find $\tan \theta$ , given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Evaluate the function requested. Write your answer as a fraction in lowest terms. - $Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find \cos B .$ Find $\cos B$ .

Provide an appropriate response. -Find the complement of an angle whose measure is $38 ^ { \circ }$ .

Solve the problem for the given information. -Find the equation of a line passing through the origin and making a $45 ^ { \circ }$ angle with the positive x-axis.

Find the measure of each angle in the problem. -

Solve the problem. -From the top of a vertical tower, 362 feet above the the surface of the earth, the angle of depression to a doghouse is $27 ^ { \circ } 20 ^ { \prime }$ . How far is it from the doghouse to the foot of the tower? Round your answer to the hundredths place when necessary.

Perform the calculation. - $79 ^ { \circ } 58 ^ { \prime } + 322 ^ { \circ } 33 ^ { \prime }$

Perform the calculation. - $90 ^ { \circ } - 38 ^ { \circ } 21 ^ { \prime }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -Find a formula for the area of the figure in terms of s.

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

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Exam 5: Trigonometric Functions

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - tan⁡θ=2.0525017\tan \theta = 2.0525017tanθ=2.0525017

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - a=17.2 cm, b=25.7 cm\mathrm { a } = 17.2 \mathrm {~cm} , \mathrm {~b} = 25.7 \mathrm {~cm}a=17.2 cm, b=25.7 cm Round the missing side length to one decimal place.

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. - csc⁡(−122∘)\csc \left( - 122 ^ { \circ } \right)csc(−122∘) and cot⁡(−122∘)\cot \left( - 122 ^ { \circ } \right)cot(−122∘)

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 \geq 0 ; \quad−7x−5y=0,x≥0; Find cos⁡θ\cos \thetacosθ

Convert the angle to degrees, minutes, and seconds. - 355.52∘355.52 ^ { \circ }355.52∘

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, rx\frac { \mathrm { r } } { \mathrm { x } }xr​

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 13∘58′13 ^ { \circ } 58 ^ { \prime }13∘58′ . If the dam is 1732 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

Use the fundamental identities to find the value of the trigonometric function. -Find tan⁡θ\tan \thetatanθ , given that sin⁡θ=34\sin \theta = \frac { 3 } { 4 }sinθ=43​ and θ\thetaθ is in quadrant II.

Evaluate the function requested. Write your answer as a fraction in lowest terms. - Find cos⁡B\cos BcosB .

Provide an appropriate response. -Find the complement of an angle whose measure is 38∘38 ^ { \circ }38∘ .

Solve the problem for the given information. -Find the equation of a line passing through the origin and making a 45∘45 ^ { \circ }45∘ angle with the positive x-axis.