Functions!

    The first thing you need to know about the unit circle are the basic functions of the circle which are Sine, Cosine, Tangent, Cosecent, Secant, and Cotangent. Which are abbreviated as sin, cos, tan, csc, sec, cot respectively. Sin, and Cos are the main ones followed by Tan. Sine and Cos will help you find the rest.  

Triangles!

    There are 2 main triangles that you need to learn, and it helps to memorize, to learn to use the unit circle. These two triangles are called the 30-60-90 triangle and the 45-45-90 triangle. (Note both are right triangles) These two triangles look like this... for the unit circle you can pretend the a's and s's are 1's.

Functions and Triangles!

To use the triangles above you have to know how to use the functions. To do this you need to know the sides of the triangle the longest side is the hypotenuse, the side across from the angle is opposite and the side touching the angle is adjacent. The functions are as follows: Sine (sin) is opposite/hypotenuse, Cosine (cos) is adjacent/hypotenuse, and Tangent (tan) is opposite/adjacent. To remember this you can use the mnemonic SOH-CAH-TOA. The other three functions are inverses of the first one. Cosecent (csc) is hypotenuse/opposite, Secent (sec) is hypotenuse/adjacent and Cotangent (cot) is adjacent/opposite. When finding 30 or 60 degree angle, or a multiple of one (or the radian match) you use the 30-60-90 triangle (above left) when finding a 45 degree angle or multiple of one (or radian match) you use the 45-45-90 triangle. (above right).