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5. Find the Cartesian equation of the curve

label Calculus
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schedule 0 Hours
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Consider the following.

x = sin 
1
2
θ,    y = cos 
1
2
θ,    −π ≤ θ ≤ π
 Eliminate the parameter to find a Cartesian equation of the curve.
Apr 4th, 2015

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: x2 + y2 = (1/4)*sin2θ + (1/4)*cos2θ = 1/4.

Answer: x2 + y2 = 1/4.


Apr 4th, 2015

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

Apr 4th, 2015

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.

Apr 4th, 2015

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Apr 4th, 2015
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