Convert the following polar equation into a cartesian equation. Specifically describe the graph of the equation in rectangular coordinates: r=5\sin\theta

Tyra 2021-04-03 Answered
Convert the following polar equation into a cartesian equation. Specifically describe the graph of the equation in rectangular coordinates: r=5sinθ
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Expert Answer

liannemdh
Answered 2021-04-05 Author has 106 answers

Step 1
To convert from polar to Cartesian from.
Step 2
Given:
r=5sinθ
Step 3
Formula used,
x=rcosθandy=rsin0
r2=x2+y2
Step 4
Simplify as,
r=5sinθ
Multiply by r as,
r2=5rsinθ
x2+y2=5(rsinθ)   (since,r2=x2+y2)
x2+y2=5y   (since,y=(rsinθ))
x2+y25y=0
x2+y25y+254=254
x2+(y52)2=(52)2
Step 5
Hence, the Cartesian form of the equation is x2+(y52)2=(52)2 which is the equation of circle with center (0,52) and radius 52.

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