Convert the cartesian equation x 2 + y 2 + 2y = 0 to a polar equation. r = -2cosθ r = -2sinθ r = -2cosθsinθ

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 getrcos2ϕ−2cosϕ=0rcos⁡2ϕ−2cos⁡ϕ=0

or

r=2cosϕcos2ϕr=2cos⁡ϕcos⁡2ϕ

The variables should add up to equal 1

62926281916 inches of rain: )