How do you convert radian measures to degrees?

2 Answers
Mar 19, 2018

#"see explanation"#

Explanation:

#"to convert from "color(blue)"radians to degrees"#

#color(red)(bar(ul(|color(white)color(black)("degrees "="radians "xx180^@/pi)color(white)(2/2)|)))#

#"to convert from "color(blue)"degrees to radians"#

#color(red)(bar(ul(|color(white)(2/2)color(black)("radians "="degrees "xxpi/180^@)color(white)(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

#pi/x=180/45#. Then #x=(45pi)/180=pi/4#. So #45º=pi/4 rad#

By the other hand, if we have #pi/3# rads, to convert to degrees, we use the same equivalence

#pi/(pi/3)=180/y#. Trasposing terms #y=(180pi)/(3pi)=180/3=60º#