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Found in: Page 478

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Find the degree measure of the angle with the given radian measure.$\frac{5\pi }{18}$

${\mathbf{50}}^{°}$

See the step by step solution

## Step 1. Given information.

$\frac{5\pi }{18}$ 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 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 $\left(\frac{{180}^{\circ }}{\pi }\right)$:

$\frac{5\pi }{18}\text{rad}=\left(\frac{5\pi }{18}\text{\hspace{0.17em}x\hspace{0.17em}}\frac{180}{\pi }\right)$

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

$\begin{array}{l}={\left(\frac{5\text{\hspace{0.17em}}x\text{\hspace{0.17em}}3.14}{18}x\frac{180}{3.14}\right)}^{\circ }\\ ={\left(\frac{5x180}{18}\right)}^{{}^{\circ }}\\ ={50}^{{}^{\circ }}\end{array}$