Eliminate the Parameter x=sin(1/2t) , y=cos(1/2t)

Math
,
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 of .
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Cancel the common factor.
Rewrite the expression.
Multiply both sides of the equation by .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Replace in the equation for to get the equation in terms of .
Simplify .
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Cancel the common factor of .
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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)

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