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

Dec 10, 2015

Recall:
${360}^{\circ} = 2 \pi$ $r a \mathrm{di} a n s$, ${180}^{\circ} = \pi$ $r a \mathrm{di} a n s$

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

$\frac{- 4 \pi}{3} \cdot {180}^{\circ} / \pi$

$= \frac{- 4 \textcolor{red}{\cancel{\textcolor{b l a c k}{\pi}}}}{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{3}}}} \cdot {\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{{180}^{\circ}}}}}^{{60}^{\circ}} / \textcolor{red}{\cancel{\textcolor{b l a c k}{\pi}}}$

$= - 4 \cdot {60}^{\circ}$

$= - {240}^{\circ}$