Pre-Calculus - Convert Between Degrees and Radians

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

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

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

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

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

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

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

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

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

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

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

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

Explanation

To convert from degrees to radians, you do:

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

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?

$150^{\circ}$

$180^{\circ}$

$250^{\circ}$

$210^{\circ}$

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: $150^{\circ}$

Convert the following to degrees:

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

$210^\circ$

$225^\circ$

$180^\circ$

$270^\circ$

Explanation

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

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

Convert degrees into radians.

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

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

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

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

Explanation

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

Therefore:

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

Please convert the following angle to degrees:

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

$210^\circ$

$240^\circ$

$180^\circ$

$176^\circ$

$260^\circ$

Explanation

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

In this case:

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

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

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

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

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

$\pi$

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

Explanation

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

In this case:

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

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?

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

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

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

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

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

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

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

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

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

$\frac{4}{3}$

$\frac{43200}{\pi }$

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:

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

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

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

$\frac{\pi }{3}$

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

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

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

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.

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

$360x=2\pi (50)$

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

Convert Between Degrees and Radians

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