Cosecant, Secant, and Cotangent Exact Values, and Coterminal Exact Values

Yesterday, we discussed how to find exact values of sine, cosine, and tangent using values on the unit circle. Today, we did the same thing except with their inverses: cotangent, cosecant, and secant.

Since we know that, in a coordinate pair (x,y)
 sine = the y value
cosine = the x value
tangent = y/x

We can use the inverses and say that:
cosecant = 1/y
secant = 1/x
cotangent = x/y

Sometimes, the radian that we convert to won't be located within the 0-360 degrees that we see on a unit circle. For example, 13pi/3 converts to 780 degrees, so that would be way off of 360, which is the last degree measure on the unit circle. In this case, we must use properties of coterminal angles to solve. Simply subtract 360 until you get a measurement that is on the Unit Circle (in this case, 780's coterminal angle would be 60 degrees). Then use the (x, y) coordinates for the coterminal angle instead.