The Basic Trig Functions

First let's define the six trig functions: sine, cosine, tangent, secant, cotangent and cosecant, and see what they have to do with triangles. The mnemonic SOH-CAH-TOA captures the definitions of the three most common trig functions, at least for angles in the first quadrant (between 0 and $\pi/2$ radians).  You will need to know the following:

$$\text{Sine }=\frac{\text{Opposite}}{\text{Hypotenuse}}$$ $$\displaystyle \text{Cosine }= \frac{\text{Adjacent}}{\text{Hypotenuse}}$$ $$\displaystyle \text{Tangent }= \frac{\text{Opposite}}{\text{Adjacent}}$$

The other trig functions are defined as reciprocals of the first three, and below you will find the reciprocal relationships (which you need to know) as well as the resulting triangle relationships of the other three trig functions.  You need not memorize the triangle relationships of these trig functions, as long as you know the reciprocal relationships. (The colorful diagram is interesting, but you need not worry about it.)

$$\text{Secant }= \frac{1}{\text{Cosine}} = \frac{\text{Hypotenuse}}{\text{Adjacent}}$$ $$\text{Cosecant }= \frac{1}{\text{Sine}} = \frac{\text{Hypotenuse}}{\text{Opposite}}$$ $$\text{Cotangent }= \frac{1}{\text{Tangent}} = \frac{\text{Adjacent}}{\text{Opposite}}$$

This video will show how to find values of trig functions in the unit circle.