SOLUTION: Find the Cartesian equation of r = 4(1 + sinθ)

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Question 1119695: Find the Cartesian equation of r = 4(1 + sinθ)
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
r=4%281%2Bsin%28theta%29%5E%22%22%29

Then use this picture:

 

Note: When trig ratios are involved, leave r as it is, and
wait until last to substitute for r:

r=4%281%2By%2Fr%29

r=4%2B4y%2Fr

Multiply through by r

r%5E2=4r%2B4y%29

Finally substitute for r:

          r=sqrt%28x%5E2%2By%5E2%29
          r%5E2=x%5E2%2By%5E2
          

Substituting in

r%5E2=4r%2B4y%29

We get

x%5E2%2By%5E2=4sqrt%28x%5E2%2By%5E2%29%2B4y

Edwin