Rewrite the polar equation r=5\sin (θ)r=5\sin (θ) as a Cartesian equation.

ankarskogC

ankarskogC

Answered question

2021-06-08

Rewrite the polar equation r=5sin(θ)r=5sin(θ) as a Cartesian equation.

Answer & Explanation

coffentw

coffentw

Skilled2021-06-09Added 103 answers

Step 1
To express the given curve in cartesian coordinates (x and y), using the transformation equations from the polar to the cartesian
Step 2
Transformation equations:
x=rcos0,y=rsin0,r2=x2+y2...(1)
Given
r=5sin0...(2)
Step 3
Mutiply (2) by r and use the relation r2=x2+y2 to obtain the required Cartesian equation
r×(2):r2=5rsin0
Apply (1) to get
x2+y2=5y, or
x2+y25y=0
Step 4
Answer: x2+y25y=0
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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