What is (7pi)/12  radians in degrees?

Mar 13, 2018

${105}^{\circ}$

Explanation:

If one revolution is $2 \pi$ radians, and it is also ${360}^{\circ}$, we can make a conversion factor:

(7cancel(pi))/12 cancel("rad")*(360^@)/(2cancel(pi) cancel("rad"))

This lets us cancel out the pi's and the radians, to give us just degrees. Now, we can reduce the fraction as much as possible before completing the conversion:

$\frac{7}{12} \cdot {360}^{\circ} / 2 \Rightarrow \frac{7}{12} \cdot {180}^{\circ}$

$7 \cdot {180}^{\circ} / 12 \Rightarrow 7 \cdot {15}^{\circ} = {105}^{\circ}$