# How do you find sintheta and tantheta if the terminal side of theta lies along the line y=-3x in QIV?

Mar 1, 2018

See exdplanation.

#### Explanation:

$Q I V$ is the quadrant where $x > 0$ and $y < 0$, so the example point can be $\left(1 , - 3\right)$

To calculate the 6 functions we have to calculate the distance between the point and the origin:

$r = \sqrt{{1}^{2} + {\left(- 3\right)}^{2}} = \sqrt{1 + 9} = \sqrt{10}$

Now we can calculate the functions:

$\sin \alpha = \frac{y}{r} = \frac{- 3}{\sqrt{10}} = - \frac{3 \sqrt{10}}{10}$

$\cos \alpha = \frac{x}{r} = \frac{1}{\sqrt{10}} = \frac{\sqrt{10}}{10}$

$\tan \alpha = \frac{y}{x} = - \frac{3}{1} = - 3$

$\cot \alpha = \frac{x}{y} = \frac{1}{- 3} = - \frac{1}{3}$

$\sec \alpha = \frac{r}{x} = \sqrt{10}$

$\csc \alpha = \frac{r}{y} = \frac{\sqrt{10}}{- 3} = - \frac{\sqrt{10}}{3}$