Consider the following.

If x = (1/2) sin θ; y = (1/2) cos θ; – π <= θ <= π are parametric equations of a curve, then

take the squares of x and y and add them: x^{2} + y^{2} = (1/4)*sin^{2}θ + (1/4)*cos^{2}θ = 1/4.

Answer: x^{2} + y^{2} = 1/4.

This answer is not correct on my homework? Do you know why?

Maybe the parametric equations are not x = (1/2)cost; y =(1/2)sint. I am sorry but the fractions in your message do not look quite readable.

If x = cos(t/2) and y = sin(t/2), then the equation will be x^2 + y^2 = 1.

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