Question

Find the degree measure of the angle with the given radian measure.

$-2$

Short answer

$\mathbf{-}\mathbf{114}\mathbf{.}{\mathbf{65}}^{\mathbf{\circ }}$

Step-by-step solution

Step 1. Given information.

The given radian measure is $-2$rad.

Step 2. Explanation.

We know that

$1\text{\hspace{0.17em}radian\hspace{0.17em}=\hspace{0.17em}}\left(\frac{{180}^{\circ }}{\pi }\right)$

Thus to find the degrees of the angle multiply the radian measure with$\left(\frac{{180}^{\circ }}{\pi }\right)$

Here in the radian measure $\mathrm{\pi }$is not available so when we multiply put $\pi =3.14$.

Step 3. Calculation.

To convert radians to degrees, multiply by$\left(\frac{{180}^{\circ }}{\pi }\right)$:

$-2\text{rad}=-\left(2\text{\hspace{0.17em}x\hspace{0.17em}}\frac{180}{\pi }\right)$

Put$\pi =3.14$ in the expression, we get:

$$\begin{gathered} =-{\left(2x\frac{180}{3.14}\right)}^{\circ } \\ =-{\left(\frac{360}{3.14}\right)}^{\circ } \\ =-{114.65}^{\circ } \end{gathered}$$