Finding Exact Values of Sine, Cosine, and Tangent on a Unit Circle

The unit circle is a circle on the coordinate plane whose radius is "1." We like the number 1 as a radius because it's super-simple and, generally, the easiest non-zero whole number to work with. The unit circle looks like this:

and we began class by making a reference picture to fill in all the exact coordinates of the unit circle. Will we ever be tested on any angle measures BESIDES the ones on the unit circle? NO. These are the most common and the only ones that you need.

From prior knowledge, we know that sin = y, cos = x, and tan = y/x. So to find the exact trig values for a given angle in degrees or radians, simply insert your y value if you're finding sine or your x value if you're finding cosine. Tangent is a little more tricky: you have to simplify y/x and divide your fractions. More often than not, something will cancel out.