Suggested languages for you:

Americas

Europe

Q26.

Expert-verifiedFound in: Page 478

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.**

$\frac{5\pi}{18}$

${\mathbf{50}}^{\xb0}$

The given radian measure is:

$\frac{5\pi}{18}$ rad.

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 $\pi =3.14$

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:

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

94% of StudySmarter users get better grades.

Sign up for free