Answer
1. $sin\frac{11\pi}{4}= \frac{\sqrt 2}{2}$.
2. $cos\frac{11\pi}{4}= -\frac{\sqrt 2}{2}$.
3. $tan\frac{11\pi}{4}= -1$.
4. $cot\frac{11\pi}{4}= -1$.
5. $sec\frac{11\pi}{4}= -\sqrt 2$.
6. $csc\frac{11\pi}{4}= \sqrt 2$.
Work Step by Step
1. $sin\frac{11\pi}{4}=sin(2\pi+\pi-\frac{\pi}{4})=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$.
2. $cos\frac{11\pi}{4}=cos(2\pi+\pi-\frac{\pi}{4})=-cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$.
3. $tan\frac{11\pi}{4}=tan(2\pi+\pi-\frac{\pi}{4})=-tan\frac{\pi}{4}=-1$.
4. $cot\frac{11\pi}{4}=\frac{1}{tan\frac{11\pi}{4}}=-1$.
5. $sec\frac{11\pi}{4}=\frac{1}{cos\frac{11\pi}{4}}=-\sqrt 2$.
6. $csc\frac{11\pi}{4}=\frac{1}{sin\frac{11\pi}{4}}=\sqrt 2$.