Algebra and Trigonometry 10th Edition

(a) complement: $\frac{\pi}{3}$ supplement: $\frac{5\pi}{6}$ (b) There is no complement of $\frac{3\pi}{4}$ because $\frac{3\pi}{4}\gt\frac{\pi}{2}$ supplement: $\frac{\pi}{4}$
(a) complement: $\frac{\pi}{2}-θ=\frac{\pi}{2}-\frac{\pi}{6}=\frac{(3)\pi}{(3)2}-\frac{\pi}{6}=\frac{3\pi}{6}-\frac{\pi}{6}=\frac{2\pi}{6}=\frac{2\pi}{2(3)}=\frac{\pi}{3}$ supplement: $\pi-θ=\pi-\frac{\pi}{6}=\frac{6\pi}{6}-\frac{\pi}{6}=\frac{5\pi}{6}$ (b) complement: There is no complement of $\frac{3\pi}{4}$ because $\frac{3\pi}{4}\gt\frac{\pi}{2}$ supplement: $\pi-θ=\pi-\frac{3\pi}{4}=\frac{4\pi}{4}-\frac{3\pi}{4}=\frac{\pi}{4}$