Question

how many degrees is 3pi/5

Answer 1

Think of the circumference of a circle with unit radius.

\(C = 2 \pi \)

Since \(2\pi\) means the entire path around a circle, then

\(2 \pi ~rad = 360^o\)

or

\(\pi~ rad = 180 ^o\)

Use the last equation above as a conversion factor.

Answer 2

\( \dfrac{\pi ~rad}{180^o} = \dfrac{180^o}{\pi ~rad} = 1\)

To convert from radians to degrees or from degrees to radians, multiply the given angle measurement by the fraction above that will cancel the units you don't want and will give the units you want.

Answer 3

Example 1. Convert 5pi/7 to degrees.

\(\dfrac{5 \pi ~\cancel{rad}}{7} \times \dfrac{180^o}{\pi~\cancel{rad}} = \dfrac{900^o}{7}\)

Example 2. Convert 225 deg to radians.

\(225^\cancel{o} \times \dfrac{\pi~rad}{180^\cancel{o}} = 1.25~rad\)

Answer 4

Thank you so much!!

Answer 5

You are very welcome.