Answer
1. $sin\frac{5\pi}{6}= \frac{1}{2}$.
2. $cos\frac{5\pi}{6}= -\frac{\sqrt 3}{2}$.
3. $tan\frac{5\pi}{6}= -\frac{\sqrt 3}{3}$.
4. $cot\frac{5\pi}{6}= -\sqrt 3$.
5. $sec\frac{5\pi}{6}= -\frac{2\sqrt 3}{3}$.
6. $csc\frac{5\pi}{6}= 2$.
Work Step by Step
1. $sin\frac{5\pi}{6}=sin(\pi-\frac{\pi}{6})=sin\frac{\pi}{6}=\frac{1}{2}$.
2. $cos\frac{5\pi}{6}=cos(\pi-\frac{\pi}{6})=-cos\frac{\pi}{6}=-\frac{\sqrt 3}{2}$.
3. $tan\frac{5\pi}{6}=tan(\pi-\frac{\pi}{6})=-tan\frac{\pi}{6}=-\frac{\sqrt 3}{3}$.
4. $cot\frac{5\pi}{6}=cot(\pi-\frac{\pi}{6})=-cot\frac{\pi}{6}=-\sqrt 3$.
5. $sec\frac{5\pi}{6}=\frac{1}{cos\frac{5\pi}{6}}=-\frac{2\sqrt 3}{3}$.
6. $csc\frac{5\pi}{6}=\frac{1}{sin\frac{5\pi}{6}}=2$.
