What is (-4pi)/3 radians in degrees?

1 Answer
Dec 10, 2015

Recall:
360^@=2pi radians, 180^@=pi radians

To convert (-4pi)/3 to degrees, multiply the fraction by 180^@/pi. Keep in mind that 180^@/pi has a value of 1, so the answer does not change. Instead, only the units are changed:

(-4pi)/3 * 180^@/pi

=(-4color(red)cancelcolor(black)pi)/color(green)cancelcolor(black)3 * color(green)cancelcolor(black)(180^@)^(60^@)/color(red)cancelcolor(black)pi

=-4*60^@

=-240^@