Convert the rectangular equation x + y = 5 to a polar equation that expresses r

Lewis Harvey

Lewis Harvey

Answered question

2021-09-30

Convert the rectangular equation x + y = 5 to a polar equation that expresses r in terms of θ.

Answer & Explanation

stuth1

stuth1

Skilled2021-10-01Added 97 answers

Step 1
We have to convert the rectangular equation x+y=5 to a polar equation that expresses r in terms of θ.We know that x-coordinate of the rectangular equation is rcosθ in polar equation and y-coordinate is rsinθ.

Therefore putting x=rcosθ,y=rsinθ in rectangular equation, we get
x+y=5
cos0+rsin0=5
Step 2
Simplifying further,
rcos0+rsin0=5
r(cos0+sin0)=5
r=5cos0+sin0
Hence, required polar equation that expresses r in terms of θ is r=5cos0+sin0.
Note:
(x,y)(rcos0,rsin0)
Where,
r=x2+y2,tan0=(yx)

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