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Precalculus : Pre-Calculus

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Find The Measure Of A Coterminal Angle

Find the coterminal angle of 15 degrees in standard position from the following answers.

Possible Answers:

$-705^{\circ}$

$365^{\circ}$

$360^{\circ}$

$-1060^{\circ}$

$30^{\circ}$

Correct answer:

$-705^{\circ}$

Explanation:

To determine the coterminal angle, simply add or subtract increments or decrements of 360 degrees to the given angle.

For n=1,2,3,... :

15+360n= 375,735,1095...

15-360n= -345,-705,-1065...

These angles can all be coterminal to 15 degrees. The only answer is .

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Example Question #301 : Pre Calculus

Find the coterminal angle of $10^\circ$ , if possible.

Possible Answers:

$\textup{The coterminal angle does not exist.}$

$-190^\circ$

$350^\circ$

$-350^\circ$

$190^\circ$

Correct answer:

$-350^\circ$

Explanation:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

10+360=370

10-360=-350

The only correct answer is .

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Example Question #6 : Find The Measure Of A Coterminal Angle

Which of the following angles is coterminal to $65^{\circ}$ ?

Possible Answers:

$-65^{\circ}$

$-425^{\circ}$

$295^{\circ}$

$-295^{\circ}$

Correct answer:

$-295^{\circ}$

Explanation:

Which of the following angles is coterminal to $65^{\circ}$ ?

Coterminal angles are angles which start and end at the same point. In other words, they share both their starting and ending point. Note, this doesn't require them to be the same angle.

For instance, $120^{\circ}$ is coterminal with $-240^{\circ}$ , because they both start on the positive x-axis, and end at the same place in quadrant 2.

So, we want to find an angle that ends at the same place in quadrant 1 as $65^{\circ}$ . Of the answer choices, only 1 ends in quadrant 1, so that one must be our answer: $-295^{\circ}$

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Example Question #1 : Angle Measures In Degrees And Radians

Convert $240^{\circ}$ to radians.

Possible Answers:

$\frac{43200}{\pi }$

$\frac{4}{3}$

$\frac{3}{4}\pi$

$\frac{4}{3}\pi$

Correct answer:

$\frac{4}{3}\pi$

Explanation:

In order to solve this problem, we must know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

with this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}}) \times 240^{\circ}=\frac{4}{3}\pi$

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Example Question #1 : Convert Between Degrees And Radians

Convert $330^{\circ}$ to radians.

Possible Answers:

$\frac{6}{11}\pi$

$\frac{11}{6}\pi$

$\frac{59400}{\pi }$

$\frac{11}{6}$

Correct answer:

$\frac{11}{6}\pi$

Explanation:

In order to solve this problem, we need to know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

using this formula, we can find our answer:

$(\frac{\pi }{180^{\circ}})\times330^{\circ}= \frac{11}{6}\pi$

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Example Question #3 : Angle Measures In Degrees And Radians

Convert $\frac{5}{6}\pi$ to degrees.

Possible Answers:

$216^{\circ}$

$150\pi$

$150^{\circ}$

$\frac{\pi }{216}$

Correct answer:

$150^{\circ}$

Explanation:

In order to solve this problem, we need to know that

$\text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$

using this formula, we can find our answer:

$(\frac{180^{\circ}}{\pi }) \times \frac{5\pi }{6}= 150^{\circ}$

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Example Question #2 : Angle Measures In Degrees And Radians

Convert $180^{\circ}$ to radians.

Possible Answers:

$\frac{1}{\pi }$

$180\pi$

$\pi$

$3\pi$

$2\pi$

Correct answer:

$\pi$

Explanation:

To solve this problem, we need to know that

$\text{Radians}=(\frac{\pi }{180^{\circ}})\times \text{Degrees}$

we can arrive to our answer by using this formula:

$(\frac{\pi }{180^{\circ}})\times 180^{\circ}=\pi$

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Example Question #5 : Angle Measures In Degrees And Radians

Convert $\frac{3\pi }{2}$ to degrees.

Possible Answers:

$120^{\circ}$

$45^\circ$

$270\pi$

$270^{\circ}$

$120\pi$

Correct answer:

$270^{\circ}$

Explanation:

In order to solve this problem, we need to know that

$\text{Degrees}=(\frac{180^{\circ}}{\pi })\times \text{Radians}$

we can arrive to our answer by using this formula:

$(\frac{180^{\circ}}{\pi })\times (\frac{3\pi }{2})=270^{\circ}$

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Example Question #3 : Angle Measures In Degrees And Radians

Find $90^{\circ}$ expressed as radians.

Possible Answers:

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\pi$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

To convert from degrees into radians,

multiply the angle in degrees by $\frac{\pi}{180}$

$90\cdot \frac{\pi}{180}=\frac{\pi}{2}$

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Example Question #5 : Convert Between Degrees And Radians

Convert the following to degrees:

$\frac{7\pi}{6}$

Possible Answers:

$180^\circ$

$270^\circ$

$225^\circ$

$210^\circ$

Correct answer:

$210^\circ$

Explanation:

To convert, multiply by the conversion factor $\frac{180}{\pi}$ .

$\frac{7\pi}{6}*\frac{180}{\pi}=7*30=210$

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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #2 : Find The Measure Of A Coterminal Angle

Example Question #301 : Pre Calculus

Example Question #6 : Find The Measure Of A Coterminal Angle

Example Question #1 : Angle Measures In Degrees And Radians

Example Question #1 : Convert Between Degrees And Radians

Example Question #3 : Angle Measures In Degrees And Radians

Example Question #2 : Angle Measures In Degrees And Radians

Example Question #5 : Angle Measures In Degrees And Radians

Example Question #3 : Angle Measures In Degrees And Radians

Example Question #5 : Convert Between Degrees And Radians

All Precalculus Resources

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