# Eliminate the Parameter x=cos(t) y=sin(t)

Set up the parametric equation for to solve the equation for .
Rewrite the equation as .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Replace in the equation for to get the equation in terms of .
Simplify .
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Divide by .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Eliminate the Parameter x=cos(t) y=sin(t)