,

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

Rewrite the equation as .

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 .

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)