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OverLord2011 [107]
3 years ago
15

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

Mathematics
1 answer:
Kisachek [45]3 years ago
3 0
R2(<span>cos2</span>ϕ−<span>sin2</span>ϕ)−2rcosϕ=0<span><span>r2</span>(<span>cos2</span>⁡ϕ−<span>sin2</span>⁡ϕ)−2rcos⁡ϕ=0</span>

<span><span><span>r2</span>cos<span>(2ϕ)</span>−2rcosϕ=0</span><span><span>r2</span>cos⁡<span>(2ϕ)</span>−2rcos⁡ϕ=<span>0

Now </span></span></span> divide through by <span><span>r≠0</span><span>r≠0</span></span> and get

<span><span>rcos<span>2ϕ</span>−2cosϕ=0</span><span>rcos⁡<span>2ϕ</span>−2cos⁡ϕ=0</span></span>

or

<span><span>r=2<span><span>cosϕ</span><span>cos<span>2ϕ</span></span></span></span><span>r=2<span><span>cos⁡ϕ</span><span>cos⁡<span>2<span>ϕ</span></span></span></span></span></span>

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