What and how do you find the coordinates to 5pi/4 and -pi/4?

Question

Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t, whenever possible. (If an answer is undefined, enter UNDEFINED.)

t=5pi/4 and t= -pi/4

Answer 1

If you have a point on the unit circle, then you can determine the coordinates by caculating the lengths of the two legs. Remember that on the unit circle any point can be described by creating a triangle with hypotenuse=1. Then, assuming α is the angle from the horizontal, x is the length of the adjacent line segment, and y is the length of the opposite line segment:

sin(α) = y/1, or sin(α) = y. Solve for y.

cos(α) = x/1, or cos(α) = x. Solve for x.

tan(α) = y/x

Solve for your two angles.