# How do you change (-3pi)/2 radians to degree measure?

May 16, 2015

To convert a radian measure to degrees, multiply by $\frac{180 \setminus {\quad}^{o}}{\pi \setminus \quad \setminus \textrm{r a \mathrm{di} a n s}}$

$\frac{- 3 \pi}{2} \setminus \textrm{r a \mathrm{di} a n s} = \frac{- 3 \pi}{2} \setminus \textrm{r a \mathrm{di} a n s} \cdot \frac{180 \setminus {\quad}^{o}}{\pi \setminus \quad \setminus \textrm{r a \mathrm{di} a n s}} = - 270 \setminus {\quad}^{o}$

,

In the multiplication, the unit of radians cancels out which leaves the result in terms of degrees.

There are $180$ degrees in $\pi$ radians. Therefore, multiplying by

$\frac{180 \setminus {\quad}^{o}}{\pi \setminus \quad \setminus \textrm{r a \mathrm{di} a n s}}$ is the same as multiplying by $1$ which doesn't change

the actual size of the angle.