How do you convert r = 3r=3 into rectangular form?

1 Answer
Gió
Nov 28, 2015

I found: x^2+y^2=9x2+y2=9

Explanation:

Consider the following diagram:

enter image source here
We can see that the relationships between rectangular and polar coordinates are:
r=sqrt(x^2+y^2)r=√x2+y2
theta=arctan(y/x)θ=arctan(yx)
and:
x=rcos(theta)x=rcos(θ)
y=rsin(theta)y=rsin(θ)

Given our expression:
r=3r=3
using our relationships of conversion.
sqrt(x^2+y^2)=3√x2+y2=3
square both sides:
x^2+y^2=9x2+y2=9

which is a circle centred in the origin and with radius of sqrt(9)=3√9=3.

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