# The terminal side of theta in standard position contains (3,0), how do you find the exact values of the six trigonometric functions of theta?

Jun 19, 2018

See explanation.

#### Explanation:

If you have a point ion the terminal side $\left(x , y\right)$ then you have to calculate the didtance between the point and the origin

## $r = \sqrt{{x}^{2} + {y}^{2}}$

$r = \sqrt{{0}^{2} + {3}^{2}} = 3$

Now the trig functions are defined as:

## $\sin \theta = \frac{y}{r}$

$\sin \theta = \frac{0}{3} = 0$

## $\cos \theta = \frac{x}{r}$

$\cos \theta = \frac{3}{3} = 1$

## $\tan \theta = \frac{y}{x}$

$\tan \theta = \frac{0}{3}$

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

$\cot \theta = \frac{3}{0}$ $\cot \theta$ is undefined.

## $\sec \theta = \frac{r}{x}$

$\sec \theta = \frac{3}{3} = 1$

## $\csc \theta = \frac{r}{y}$

$\csc \theta = \frac{3}{0}$ $\csc \theta$ is undefined