Answer
a. $\displaystyle \frac{3\pi}{10}$
b. $\displaystyle \frac{\pi}{8}$
c. $\displaystyle \frac{\pi}{3}$
Work Step by Step
The reference angle $\overline{\theta}$ associated with an angle $\theta$
is the acute angle formed by the terminal side of $\theta$ and the x-axis.
a.
$\displaystyle \frac{7\pi}{10}$ has terminal side in quadrant II.
The acute angle it forms with the x-axis is
$\displaystyle \overline{\theta}=\pi-\frac{7\pi}{10}=\frac{3\pi}{10}.$
b.
$\displaystyle \frac{9\pi}{8}$ has terminal side in quadrant III.
The acute angle it forms with the x-axis is
$\displaystyle \overline{\theta}=\frac{9\pi}{8} -\displaystyle \pi=\frac{\pi}{8}.$
c.
$\displaystyle \frac{10\pi}{3}=2\pi+\frac{4\pi}{3}$ has terminal side in quadrant III.
The acute angle it forms with the x-axis is
$\displaystyle \overline{\theta}=\frac{4\pi}{3} -\displaystyle \pi=\frac{\pi}{3}.$
