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Precalculus : Angle Measures in Degrees and Radians

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Example Questions

Example Question #82 : Trigonometric Functions

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:

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

$\frac{\pi }{3}$

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

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

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

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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Example Question #91 : Trigonometric Functions

Terry is running around a circular track. If he covers $\frac{7\pi}{6} radians$ in 120 seconds, how many degrees has he covered?

Possible Answers:

$150^{\circ}$

$255^{\circ}$

$210^{\circ}$

$270^{\circ}$

Correct answer:

$210^{\circ}$

Explanation:

Terry is running around a circular track. If he covers $\frac{7\pi}{6} radians$ in 120 seconds, how many degrees has he covered?

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

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

Where r and d are our desired angle measure in radians and degrees, respectively.

So, we have r, plug in and simplify to get d!

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

Making our answer:

$210^{\circ}$

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Example Question #11 : Convert Between Degrees And Radians

While SCUBA diving as part of a search and rescue diving operation, Daniel is responsible for covering a sector which represents $\frac{5\pi}{6}$ radians. What is this angle in degrees?

Possible Answers:

$210^{\circ}$

$150^{\circ}$

$180^{\circ}$

$250^{\circ}$

Correct answer:

$150^{\circ}$

Explanation:

While SCUBA diving as part of a search and rescue diving operation, Daniel is responsible for covering a sector which represents $\frac{5\pi}{6}$ radians. What is this angle in degrees?

Recall the following formula for converting radians to degrees:

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

Where d and r are angle measures in degrees and radians, respectively.

So, we are given a value in radians and asked to find it in degrees. Plug in to the above formula to find the answer!

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

So our answer is: $150^{\circ}$

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Example Question #11 : Angle Measures In Degrees And Radians

Determine the value of $225^\circ$ in radians.

Possible Answers:

$\frac{5\pi}{4}rad$

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

$\frac{40500}{\pi}rad$

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

Correct answer:

$\frac{5\pi}{4}rad$

Explanation:

To convert from degrees to radians, you do:

$225deg\cdot \frac{(\pi) rad}{180 deg}= \frac{(45\cdot5)\cdot\pi}{45\cdot4} rad= \frac{5\pi}{4} rad$

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Example Question #12 : Angle Measures In Degrees And Radians

Convert the following to radians.

$270^{\circ}$

Possible Answers:

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

$\frac{\pi}{3}$

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

$\frac{3}{\pi}$

Correct answer:

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

Explanation:

To solve, use the conversion factor $\frac{\pi{radians}}{180^{\circ}}$ . Thus,

$\frac{270^{\circ}}{1}\cdot \frac{\pi{radians}}{180^{\circ}}=\frac{270\pi}{180}=\frac{3\pi}{2}$

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Example Question #321 : Pre Calculus

Convert $660^{\circ}$ to radians.

Possible Answers:

$\frac{11\pi }{3}$

$\frac{13\pi }{3}$

$\frac{66\pi }{7}$

$\frac{8\pi }{3}$

$\frac{111\pi }{3}$

Correct answer:

$\frac{11\pi }{3}$

Explanation:

To convert from degrees to radians, you must multiply by $\frac{\pi }{180}$ : $660\cdot \frac{\pi }{180}$ . Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.

Thus, your answer is $\frac{11\pi }{3}$ .

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Example Question #93 : Trigonometric Functions

Convert $\frac{8\pi }{3}$ to degrees.

Possible Answers:

$550^{\circ}$

$400^{\circ}$

$440^{\circ}$

$280^{\circ}$

$480^{\circ}$

Correct answer:

$480^{\circ}$

Explanation:

To convert from radians to degrees, you must multiply by $\frac{180}{\pi }$ so that you then get $\frac{8\pi }{3}\cdot \frac{180}{\pi }$ . Then, simplify and multiply straight across so that your answer is $480^{\circ}$ .

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Example Question #91 : Trigonometric Functions

$\frac{11\pi}{9}$ radians is equivalent to how many degrees?

Possible Answers:

190

185

210

220

225

Correct answer:

220

Explanation:

The value of $\pi$ radians equal 180 degrees. Substitute and solve.

$\frac{11\pi}{9}=\frac{11\cdot 180}{9}=\frac{1980}{9}=220$

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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 #82 : Trigonometric Functions

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #91 : Trigonometric Functions

Example Question #11 : Convert Between Degrees And Radians

Example Question #11 : Angle Measures In Degrees And Radians

Example Question #12 : Angle Measures In Degrees And Radians

Example Question #321 : Pre Calculus

Example Question #93 : Trigonometric Functions

Example Question #91 : Trigonometric Functions

All Precalculus Resources

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