Pre-Calculus

1.) Which of the following polar equations is equivalent to the parametric equations below?
x=t^2
y=2t
A.) r=4cot(theta)csc(theta)
B.) r=4tan(theta)sec(theta)
C.) r=tan(theta)sec(theta)/4
D.) r=16cot(theta)csc(theta)

2.) Which polar equation is equivalent to the parametric equations below? x=sin(theta)cos(theta)+cos(theta)
y=sin^2(theta)+sin(theta)
A.) r=cos(theta)+1
B.) r=sin(theta)+1
C.) r=sin^2(theta)+1
D.) r=1-cos(theta)

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  1. First you try.

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  2. like t = y/2
    then x = t^2 = y^2/4
    so
    y^2 = 4 x
    but
    y = r sin T
    x = r cos T
    so
    r^2 sin^2 T = 4 r cos T
    r sin^2 T = 4 cos T
    r =4 cos T/sin^2T = 4 cot T csc T

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