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Precalculus : Trigonometric Functions

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Example Questions

Example Question #81 : Trigonometric Functions

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

Possible Answers:

$\pi$

$3\pi$

$2\pi$

$\frac{1}{\pi }$

$180\pi$

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:

$45^\circ$

$120\pi$

$270^{\circ}$

$270\pi$

$120^{\circ}$

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 #3 : Convert Between Degrees And Radians

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

Possible Answers:

$\pi$

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

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 #4 : Convert Between Degrees And Radians

Convert the following to degrees:

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

Possible Answers:

$210^\circ$

$180^\circ$

$270^\circ$

$225^\circ$

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 #5 : Convert Between Degrees And Radians

Convert 1140 degrees into radians.

Possible Answers:

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

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

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

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

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 #2 : Angle Measures In Degrees And Radians

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

Possible Answers:

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

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

$\pi$

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

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

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 #6 : Convert Between Degrees And Radians

Please convert the following angle to degrees:

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

Possible Answers:

$180^\circ$

$260^\circ$

$240^\circ$

$176^\circ$

$210^\circ$

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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Example Question #11 : Convert Between Degrees And Radians

Convert $\frac{3\pi}{7}$ radians to degrees. Round to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

In order to convert from radians to degrees, we will need to know how many degrees are in a radian.

$\pi \textup{ radians} = 180 \textup{ degrees}$

Substitute 180 as a replacement for $\pi$ .

$\frac{3\pi}{7} = \frac{3\times 180}{7} = \frac{540}{7} = 77.1429$

The correct answer is .

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Example Question #11 : Angle Measures In Degrees And Radians

Convert $50^{\circ}$ to radians.

Possible Answers:

$\frac{2\pi }{3}$

$\frac{\pi }{3}$

$\frac{5\pi }{18}$

$\frac{9\pi }{14}$

$\frac{5\pi }{21}$

Correct answer:

$\frac{5\pi }{18}$

Explanation:

To convert degrees to radians we must recall the conversion factor. Remember that $360^\circ=2\pi$ .

Therefore, we can create the following fraction and solve for the missing variable.

$\frac{50^{\circ}}{360^{\circ}}=\frac{x}{2\pi }$

$360x=2\pi (50)$

$x=\frac{5\pi }{18}$

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Example Question #11 : Angle Measures In Degrees And Radians

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be $114^{\circ}$ . What is the angle in radians?

Possible Answers:

$0.3\bar{3}\pi \:\uptext{radians}$

$6.\bar{3}\pi\:\uptext{ radians}$

$0.3\bar{6}\pi\:\uptext{radians}$

$0.6\bar{3}\pi \:\uptext{radians}$

Correct answer:

$0.6\bar{3}\pi \:\uptext{radians}$

Explanation:

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be $114^{\circ}$ . What is the angle in radians?

To convert from degrees to radians, use the following formula:

$\frac{d\pi}{180}=r$

Where and stand for degrees and radians, respectively.

$r=\frac{114\pi}{180}=0.6\bar{3}\pi\:\uptext{radians}$

So we get

$0.6\bar{3}\pi \:\uptext{radians}$

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Precalculus : Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #81 : Trigonometric Functions

Example Question #5 : Angle Measures In Degrees And Radians

Example Question #3 : Convert Between Degrees And Radians

Example Question #4 : Convert Between Degrees And Radians

Example Question #5 : Convert Between Degrees And Radians

Example Question #2 : Angle Measures In Degrees And Radians

Example Question #6 : Convert Between Degrees And Radians

Example Question #11 : Convert Between Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

All Precalculus Resources

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