# How do you find the sintheta for an angle in standard position if the terminal side passes through the point (-2, -5)?

Jan 30, 2017

See explanation.

#### Explanation:

If we have a point $P = \left(x , y\right)$ on the terminal side of an angle to calculate the trigonometric functions of the angle we use:

## $\cot \alpha = \frac{x}{y}$

where $r$ is the radius: $r = \sqrt{{x}^{2} + {y}^{2}}$

Here we have:

$r = \sqrt{{\left(- 2\right)}^{2} + {\left(- 5\right)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$

so

$\sin \alpha = \frac{- 5}{\sqrt{29}} = - \frac{5 \sqrt{29}}{29}$