# The point (8,15) 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?

Mar 4, 2017

sin theta = 15/17; cos theta = 8/17
tan theta = 15/8; cot theta = 8/15
csc theta = 17/15; sec theta = 17/8

#### Explanation:

Draw a right triangle in the first quadrant of the rectangular coordinate plane with base = $8$ and height = $15$.

Calculate the hypotenuse using Pythagorean Theorem:
r = sqrt (8^2 + 15^2) = sqrt(64 + 225+ = sqrt(289) = 17

Use the trig. definitions to find all of the angles:
$\sin \theta = \text{opposite"/"hypotenuse} = \frac{15}{17}$

$\cos \theta = \text{adjacent"/"hypotenuse} = \frac{8}{17}$

$\tan \theta = \text{opposite"/"adjacent} = \frac{15}{8}$

$\csc \theta = \frac{1}{\sin \theta} = \frac{17}{15}$

$\sec \theta = \frac{1}{\cos \theta} = \frac{17}{8}$

$\cot \theta = \frac{1}{\tan \theta} = \frac{8}{15}$