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Precalculus : Angle Measures in Degrees and Radians

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Example Question #1 : Convert Between Degrees And Radians

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

Possible Answers:

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

$\frac{43200}{\pi }$

$\frac{4}{3}$

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

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:

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

$\frac{11}{6}$

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

$\frac{59400}{\pi }$

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 #1 : Convert Between Degrees And Radians

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

Possible Answers:

$150^{\circ}$

$\frac{\pi }{216}$

$216^{\circ}$

$150\pi$

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 #1 : Angle Measures In Degrees And Radians

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

Possible Answers:

$\pi$

$\frac{1}{\pi }$

$3\pi$

$180\pi$

$2\pi$

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 #1 : Convert Between Degrees And Radians

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

Possible Answers:

$270\pi$

$120\pi$

$270^{\circ}$

$120^{\circ}$

$45^\circ$

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 #6 : Convert Between Degrees And Radians

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

Possible Answers:

$\frac{\pi}{6}$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

$\pi$

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 #1 : 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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Example Question #8 : Convert Between Degrees And Radians

Convert 1140 degrees into radians.

Possible Answers:

$\frac{7\pi}{3}$

$\frac{19\pi}{3}$

$\frac{19\pi}{2}$

$\frac{17\pi}{3}$

Correct answer:

$\frac{19\pi}{3}$

Explanation:

To convert between degrees and radians, you must use the following conversion factor 180 degrees = pi radians.

Therefore:

$\frac{1140}{1}*\frac{\pi}{180}=\frac{1140\pi}{180}=\frac{19\pi}{3}$

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Example Question #9 : Convert Between Degrees And Radians

Please convert the following from degrees to radians: $315^{\circ}$

Possible Answers:

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

$\frac{7\pi}{8}$

$\frac{5\pi}{3}$

$\frac{7\pi}{4}$

$\pi$

Correct answer:

$\frac{7\pi}{4}$

Explanation:

To convert from degrees to radians, multiply the input by: $\frac{\pi}{180}$

In this case:

$\frac{\pi}{180}$ $(315^{\circ}) = \frac{7\pi}{4}$

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Example Question #10 : Convert Between Degrees And Radians

Please convert the following angle to degrees:

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

Possible Answers:

$240^\circ$

$180^\circ$

$260^\circ$

$176^\circ$

$210^\circ$

Correct answer:

$210^\circ$

Explanation:

To convert from radians to degrees, multiply the input by $\frac{180}{\pi}$ .

In this case:

$\frac{180}{\pi}\cdot \left(\frac{7\pi}{6}\right) = 210^{\circ}$

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Precalculus : Angle Measures in Degrees and Radians

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Convert Between Degrees And Radians

Example Question #1 : Convert Between Degrees And Radians

Example Question #1 : Convert Between Degrees And Radians

Example Question #1 : Angle Measures In Degrees And Radians

Example Question #1 : Convert Between Degrees And Radians

Example Question #6 : Convert Between Degrees And Radians

Example Question #1 : Convert Between Degrees And Radians

Example Question #8 : Convert Between Degrees And Radians

Example Question #9 : Convert Between Degrees And Radians

Example Question #10 : Convert Between Degrees And Radians

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