Answer
(a)$-\frac{\pi}{5}$ lies in the Fourth Quadrant.
(b) $\frac{7\pi}{5}$ lies in the Third Quadrant.
Work Step by Step
If $θ$ lies in the:
- First Quadrant, then $0\ltθ\lt\frac{\pi}{2}$
- Second Quadrant, then $\frac{\pi}{2}\ltθ\lt\pi$
- Third Quadrant, then $\pi\ltθ\lt\frac{3\pi}{2}$
- Fourth Quadrant, then $\frac{3\pi}{2}\ltθ\lt2\pi$
(a) $-\frac{\pi}{5}+2\pi=\frac{9\pi}{5}$
$\frac{3\pi}{2}\lt\frac{9\pi}{5}\lt2\pi$ , so $-\frac{\pi}{5}$ lies in the Fourth Quadrant.
(b) $\pi\lt\frac{7\pi}{5}\lt\frac{3\pi}{2}$, so $\frac{7\pi}{5}$ lies in the Third Quadrant.
