How do you convert radian measures to degrees?

Mar 19, 2018

$\text{see explanation}$

Explanation:

$\text{to convert from "color(blue)"radians to degrees}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\textcolor{b l a c k}{\text{degrees "="radians } \times {180}^{\circ} / \pi}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{to convert from "color(blue)"degrees to radians}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\text{radians "="degrees } \times \frac{\pi}{180} ^ \circ} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

Mar 19, 2018

Throug the equivalence pi=180º and de direct proportionality of arcs and angles. See examples

Explanation:

If we have 45º degrees convert to radians is easy

$\frac{\pi}{x} = \frac{180}{45}$. Then $x = \frac{45 \pi}{180} = \frac{\pi}{4}$. So 45º=pi/4 rad

By the other hand, if we have $\frac{\pi}{3}$ rads, to convert to degrees, we use the same equivalence

$\frac{\pi}{\frac{\pi}{3}} = \frac{180}{y}$. Trasposing terms y=(180pi)/(3pi)=180/3=60º