Angle Measures in Degrees and Radians - Pre-Calculus

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

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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$

Convert to radians.

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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}$\pi$

Convert to radians.

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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$

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

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

using this formula, we can find our answer:

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

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

we can arrive to our answer by using this formula:

Convert to radians.

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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$

Convert the following to degrees:

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

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

$$\frac{7\pi}{6}$$\frac{180}{\pi}$=730=210$

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

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

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

Find expressed as radians.

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To convert from degrees into radians,

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

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

Convert degrees into radians.

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

Please convert the following angle to degrees:

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

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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) = $210^{\circ}$

Please convert the following from degrees to radians:

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

In this case:

$\frac{\pi}{180}$

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

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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 .

Convert to radians.

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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.

$360x=2\pi (50)$

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

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be . What is the angle in radians?

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Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be . 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:\up$\text{radians}$$

So we get

$0.6\bar{3}\pi :\up$\text{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?

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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!

So our answer is:

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

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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:

Convert the following to radians.

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To solve, use the conversion factor . Thus,

Convert to radians.

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

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

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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 .