Answer
$sin\frac{3\pi}{4}=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$
$csc\frac{3\pi}{4}=\frac{1}{sin\frac{3\pi}{4}}=\sqrt 2$
$cos\frac{3\pi}{4}=-cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$
$sec\frac{3\pi}{4}=\frac{1}{cos\frac{3\pi}{4}}=-\sqrt 2$
$tan\frac{3\pi}{4}=-tan\frac{\pi}{4}=-1$
$cot\frac{3\pi}{4}=\frac{1}{tan\frac{3\pi}{4}}=-1$
Work Step by Step
Since, $\frac{3\pi}{4}$ lies on second quadrant, thus its reference angle will be $\pi-\frac{3\pi}{4}=\frac{\pi}{4}$, which can be considered as common angle to all trigonometric ratios.
The trigonometric ratios and their inverse trigonometric ratios are given as follows:
$sin\frac{3\pi}{4}=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$
$csc\frac{3\pi}{4}=\frac{1}{sin\frac{3\pi}{4}}=\sqrt 2$
$cos\frac{3\pi}{4}=-cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$
$sec\frac{3\pi}{4}=\frac{1}{cos\frac{3\pi}{4}}=-\sqrt 2$
$tan\frac{3\pi}{4}=-tan\frac{\pi}{4}=-1$
$cot\frac{3\pi}{4}=\frac{1}{tan\frac{3\pi}{4}}=-1$
