Convert the Cartesian equation x 2 + y 2 + 2y = 0 to a polar equation.

1 answer:

3 0

R2(cos2ϕ−sin2ϕ)−2rcosϕ=0r2(cos2⁡ϕ−sin2⁡ϕ)−2rcos⁡ϕ=0

r2cos(2ϕ)−2rcosϕ=0r2cos⁡(2ϕ)−2rcos⁡ϕ=0

Now divide through by r≠0r≠0 and get

rcos2ϕ−2cosϕ=0rcos⁡2ϕ−2cos⁡ϕ=0

r=2cosϕcos2ϕr=2cos⁡ϕcos⁡2ϕ

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