# The point (4,3) 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 12, 2017

#### Answer:

Sine $= \frac{3}{5} = 0.6$
Cosine $= \frac{4}{5} = 0.8$
Tangent $= \frac{3}{4} = .75$
Cotangent =$\frac{4}{3} = 1.33$
Secant $= \frac{5}{4} = 1.25$
Cosecant $= \frac{5}{3} = 1.67$

#### Explanation:

Begin by drawing the terminal side in standard position and drawing the associated triangle.

Using the Pythagorean Theorem calculate the missing side the hypotenuse. (This is a Pythagorean Triplet 3-4-5)

We now have a triangle with values of

$x = 4$
$y = 3$
$h = 5$

The six trigonometric functions include

Sine $= \frac{y}{h}$
Cosine $= \frac{x}{h}$
Tangent $\frac{y}{x}$
Cotangent =$\frac{x}{y}$
Secant $= \frac{h}{x}$
Cosecant $= \frac{h}{y}$

Sine $= \frac{3}{5} = 0.6$
Cosine $= \frac{4}{5} = 0.8$
Tangent $= \frac{3}{4} = .75$
Cotangent =$\frac{4}{3} = 1.33$
Secant $= \frac{5}{4} = 1.25$
Cosecant $= \frac{5}{3} = 1.67$