# The point (7,24) 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?

Sep 22, 2017

See explanation.

#### Explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

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

Here it is: $r = \sqrt{{7}^{2} + {24}^{2}} = \sqrt{49 + 576} = \sqrt{625} = 25$

Now we can calculate all 6 trig, functions:

$\sin \alpha = \frac{y}{r} = \frac{24}{25}$

$\cos \alpha = \frac{x}{r} = \frac{7}{25}$

$\tan \alpha = \frac{y}{x} = \frac{24}{7} = 1 \frac{3}{7}$

$\cot \alpha = \frac{x}{y} = \frac{7}{24}$

$\sec \alpha = \frac{r}{x} = \frac{25}{7} = 3 \frac{4}{7}$

$\csc \alpha = \frac{r}{y} = \frac{25}{24} = 1 \frac{1}{24}$