,

Set up the parametric equation for to solve the equation for .

Rewrite the equation as .

Take the inverse sine of both sides of the equation to extract from inside the sine.

Multiply both sides of the equation by .

Cancel the common factor.

Rewrite the expression.

Multiply both sides of the equation by .

Cancel the common factor.

Rewrite the expression.

Replace in the equation for to get the equation in terms of .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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=sin(1/2t) , y=cos(1/2t)