Find a polar equation of the form r=f(θ) for the curve represented by the cartesian equation x=−y2.
Question
Answer:
We define the following variables:x = r * cos (θ)
y = r * sine (θ)
Substituting the variables we have:
x = -y ^ 2
r * cos (θ) = - (r * sin (θ)) ^ 2
Rewriting:
r * cos (θ) = - (r ^ 2 * sin ^ 2 (θ))
We cleared r:
r = - ((cos (θ)) / (sin ^ 2 (θ)))
We rewrite:
r = - ((cos (θ)) / (sin (θ))) * (1 / sin (θ))
r = - cot (θ) * csc (θ)
Answer:
a polar equation of the form r = f (θ) for the curve represented by the cartesian equation x = -y2 is:
r = - cot (θ) * csc (θ)
solved
general
5 months ago
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