# Is there an easy way to convert degrees to radians?

Oct 31, 2015

see explanation

#### Explanation:

It is a matter of establishing a link between the two conditions then changing the representation of that link to suit your objective.

The link is how many of each is in either $\frac{1}{2}$ a circle or if you prefer, all of a circle

There are 360 degrees in a circle.

There is $2 \pi$ radians in a circle.

These for a consistent ratio

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$\textcolor{red}{\text{Change radians to degrees:}}$ $\to \left(\text{given radians") times ("Degrees")/("Radians}\right)$

("given radians") times (360^o)/((2pi)
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$\textcolor{red}{\text{Change degrees into radians:}}$ $\to \left(\text{given degrees") times ("Radians")/("Degrees}\right)$

$\left(\text{given degrees}\right) \times \frac{2 \pi}{{360}^{o}}$
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So you just put what you wish to convert into as the top of the fraction (Numerator). A lot of people use 3.142 as an approximation for $\pi$.