Answer
$sin\frac{11\pi}{4}=\frac{\sqrt 2}{2}$ this should be $\frac{1}{\sqrt 2}$
$cos\frac{11\pi}{4}=-\frac{\sqrt 2}{2}$ this should be $\frac{1}{\sqrt 2}$
$tan\frac{11\pi}{4}=-1$
$csc\frac{11\pi}{4}=\sqrt 2$
$sec\frac{11\pi}{4}=-\sqrt 2$
$cot\frac{11\pi}{4}=-1$
Work Step by Step
The trigonometric ratios and their inverse trigonometric ratios are given as follows:
$\sin\frac{11\pi}{4}=\sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$ this should be $\frac{1}{\sqrt 2}$
$\cos\frac{11\pi}{4}=-\cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$ this should be $\frac{1}{\sqrt 2}$
$\tan\frac{11\pi}{4}=-\tan\frac{\pi}{4}=-1$ this should be $1$
$\csc\frac{11\pi}{4}=\frac{1}{\sin\frac{3\pi}{4}}=\sqrt 2$
$\sec\frac{11\pi}{4}=\frac{1}{\cos\frac{11\pi}{4}}=-\sqrt 2$
$\cot\frac{11\pi}{4}=\frac{1}{\tan\frac{11\pi}{4}}=-1$
