Answer
a. $\displaystyle \frac{2\pi}{7}$
b. $ 0.4\pi$
c. $1.4$
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.
$\displaystyle \frac{5\pi}{7}$ has terminal side in quadrant II.
The acute angle it forms with the x-axis is
$\displaystyle \overline{\theta}=\pi-\frac{5\pi}{7}=\frac{2\pi}{7}.$
b.
$-1.4\pi=-2\pi+0.6\pi$ has terminal side in quadrant II.
The acute angle it forms with the x-axis is
$\overline{\theta}=\pi-0.6\pi=0.4\pi.$
c.
$\theta=$1.4 terminates in quadrant I,
so it is the acute angle we are after, $\overline{\theta}=1.4$
