# How do you convert -115 degrees to radians?

Mar 4, 2018

${4.2832}^{c}$

#### Explanation:

Radian = (degree / 360) * 2pi

$r = \left(- \frac{115}{360}\right) \cdot \left(2 \pi\right) \approx - {2}^{c}$

$\implies 2 \pi - 2 = {4.2832}^{c}$

Mar 4, 2018

$\frac{49 \pi}{36}$, or $4.276 \text{rad}$

#### Explanation:

We can find the coterminal angle for this angle, and convert that to radians.

We have $- {115}^{\circ}$. To find the coterminal, add or subtract ${360}^{\circ}$ until ${0}^{\circ} \le x \le {360}^{\circ}$.

So we can say $- 115 + 360 = {245}^{\circ}$

To convert to radians, $r$, where the degree measure is $d$, use:

$r = \frac{\mathrm{dp} i}{180}$

And here, $d = 245$, so we can input:

$r = \frac{245 \pi}{180}$

$r = \frac{49 \pi}{36}$, or $4.276 \text{rad}$