# Eliminate the Parameter x=4cos(t) , y=4sin(t)

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Set up the parametric equation for to solve the equation for .
Rewrite the equation as .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
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 .
Simplify the numerator.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Multiply and .
Multiply by .
Rewrite as .
Factor the perfect power out of .
Factor the perfect power out of .
Rearrange the fraction .
Pull terms out from under the radical.
Combine and .
Reduce the expression by cancelling the common factors.
Divide by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Eliminate the Parameter x=4cos(t) , y=4sin(t)

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