# How do you find all six trigonometric function of theta if the point (sqrt2,sqrt2) is on the terminal side of theta?

Jun 20, 2018

As below.

#### Explanation:

$\left(x , y\right) = \left(\sqrt{2} , \sqrt{2}\right)$

$\tan \theta = \frac{y}{x} = \frac{\sqrt{2}}{\sqrt{2}} = 1 , \theta = \frac{\pi}{4}$

$\cot \theta = \cot \left(\frac{\pi}{4}\right) = \frac{1}{\tan} \left(\frac{\pi}{4}\right) = 1$

$\sin \theta = \sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$

$\cos \theta = \cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$

$\csc \left(\theta\right) = \frac{1}{\sin} \theta = \frac{1}{\sin} \left(\frac{\pi}{4}\right) = \sqrt{2}$

$\sec \left(\theta\right) = \frac{1}{\cos} \theta = \frac{1}{\cos} \left(\frac{\pi}{4}\right) = \sqrt{2}$