# The point (-sqrt3,-1) is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

Dec 30, 2016

The ratios are listed below.

#### Explanation:

The given point lies in the $I I {I}^{r d}$ quadrant as shown in the figure. The terminal side of the angle is OP.

Using Pythagoras, length of OP would come out to be 2. The angle, whose terminal side is OP, is marked in the red pen in the figure. If this angle is termed as $\theta$, then different trignometrical ratios would be as follows:

$\sin \theta = - \frac{1}{2}$

$\cos \theta = - \frac{\sqrt{3}}{2}$

$\tan \theta = \frac{- 1}{- \sqrt{3}} = \frac{1}{\sqrt{3}}$

$\csc \theta = - 2$

$\sec \theta = - \frac{2}{\sqrt{3}}$

$\cot \theta = \sqrt{3}$