Exam 6: Trigonometric Functions

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 $\sin A$ when $a = 9$ and $b = 2$ .

(Multiple Choice)

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Question 201

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. - $\cot \theta$ , given that $\tan \theta = 0.067$

(Multiple Choice)

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Question 202

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\tan 69 ^ { \circ }$

(Multiple Choice)

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Question 203

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

(Multiple Choice)

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Question 204

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

(Multiple Choice)

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Question 205

Find the measure of each angle in the problem. -Complementary angles with measures $2 x$ and $7 x - 27$ degrees

(Multiple Choice)

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Question 206

Find the exact value of the expression. - $\csc 330 ^ { \circ }$

(Multiple Choice)

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Question 207

Find the exact value of the expression. - $\csc \left( - 1020 ^ { \circ } \right)$

(Multiple Choice)

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Question 208

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $337 ^ { \circ } 9 ^ { \prime } 8 ^ { \prime \prime }$

(Multiple Choice)

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Question 209

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -From the top of a vertical tower, 355 feet above the the surface of the earth, the angle of depression to a doghouse is $27 ^ { \circ } 31 ^ { \prime }$ . How far is it from the doghouse to the foot of the tower? Round your answer to the hundredths place when necessary.

(Multiple Choice)

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Question 210

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. - $( 4,0 )$

(Multiple Choice)

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Question 211

Find the reference angle for the given angle. -186.6°

(Multiple Choice)

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Question 212

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 $\csc B$ when $a = 10$ and $b = 9$ .

(Multiple Choice)

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Question 213

Find the exact value of the expression. - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

(Multiple Choice)

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Question 214

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

(Multiple Choice)

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Question 215

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

(Multiple Choice)

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Question 216

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\tan \theta = 0.55$

(Multiple Choice)

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Question 217

Solve the problem. -An airplane travels at $120 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $312 ^ { \circ }$ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

(Multiple Choice)

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Question 218

Evaluate the expression. - $\cot \left( n \cdot 180 ^ { \circ } \right)$

(Multiple Choice)

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Question 219

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) - $( - 4,0 )$ $Sketch an angle \theta in standard position such that \theta has the least positive measure and the given point is on the terminal side of \theta (3, 6) - ( - 4,0 )$

(Multiple Choice)

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Question 220

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. - $\cot \theta$ , given that $\tan \theta = 0.067$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\tan 69 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

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

Find the measure of each angle in the problem. -Complementary angles with measures $2 x$ and $7 x - 27$ degrees

Find the exact value of the expression. - $\csc 330 ^ { \circ }$

Find the exact value of the expression. - $\csc \left( - 1020 ^ { \circ } \right)$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $337 ^ { \circ } 9 ^ { \prime } 8 ^ { \prime \prime }$

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. - $( 4,0 )$

Find the reference angle for the given angle. -186.6°

Find the exact value of the expression. - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

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

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\tan \theta = 0.55$

Solve the problem. -An airplane travels at $120 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $312 ^ { \circ }$ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

Evaluate the expression. - $\cot \left( n \cdot 180 ^ { \circ } \right)$

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

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. - cot⁡θ\cot \thetacotθ , given that tan⁡θ=0.067\tan \theta = 0.067tanθ=0.067

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - tan⁡69∘\tan 69 ^ { \circ }tan69∘

Use the fundamental identities to find the value of the trigonometric function. -Find cot⁡θ\cot \thetacotθ , given that tan⁡θ=73\tan \theta = \frac { \sqrt { 7 } } { 3 }tanθ=37​​ and θ\thetaθ is in quadrant III.

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

Find the measure of each angle in the problem. -Complementary angles with measures 2x2 x2x and 7x−277 x - 277x−27 degrees

Find the exact value of the expression. - csc⁡330∘\csc 330 ^ { \circ }csc330∘

Find the exact value of the expression. - csc⁡(−1020∘)\csc \left( - 1020 ^ { \circ } \right)csc(−1020∘)

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 337∘9′8′′337 ^ { \circ } 9 ^ { \prime } 8 ^ { \prime \prime }337∘9′8′′

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. - (4,0)( 4,0 )(4,0)

Find the reference angle for the given angle. -186.6°

Find the exact value of the expression. - cos⁡θ=−32\cos \theta = - \frac { \sqrt { 3 } } { 2 }cosθ=−23​​

Find the exact value of the expression. - tan⁡300∘\tan 300 ^ { \circ }tan300∘

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

Decide whether the statement is possible or impossible for an angle θ.\theta .θ. - tan⁡θ=0.55\tan \theta = 0.55tanθ=0.55

Solve the problem. -An airplane travels at 120 km/h120 \mathrm {~km} / \mathrm { h }120 km/h for 5hr5 \mathrm { hr }5hr in a direction of 312∘312 ^ { \circ }312∘ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

Evaluate the expression. - cot⁡(n⋅180∘)\cot \left( n \cdot 180 ^ { \circ } \right)cot(n⋅180∘)

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) - (−4,0)( - 4,0 )(−4,0)

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

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. - $\cot \theta$ , given that $\tan \theta = 0.067$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\tan 69 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ , given that $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

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

Find the measure of each angle in the problem. -Complementary angles with measures $2 x$ and $7 x - 27$ degrees

Find the exact value of the expression. - $\csc 330 ^ { \circ }$

Find the exact value of the expression. - $\csc \left( - 1020 ^ { \circ } \right)$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $337 ^ { \circ } 9 ^ { \prime } 8 ^ { \prime \prime }$

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. - $( 4,0 )$

Find the exact value of the expression. - $\cos \theta = - \frac { \sqrt { 3 } } { 2 }$

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

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

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\tan \theta = 0.55$

Solve the problem. -An airplane travels at $120 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $312 ^ { \circ }$ from Greenville. At the end of this time, how far west of Greenville is the plane (to the nearest kilometer)?

Evaluate the expression. - $\cot \left( n \cdot 180 ^ { \circ } \right)$