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