How do you convert #r = 6cosθ# into rectangular form?

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How do you convert #r = 6cosθ# into rectangular form?

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Answer 1 · 2015-11-24T00:34:43

I found: #x^2+y^2=6x#

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)#
#theta=arctan(y/x)#
and:
#x=rcos(theta)#
#y=rsin(theta)#

Given our expression:
#r=6cos(theta)#

multiply by #r# both sides:
#r^2=6rcos(theta)#
so that you get:
#x^2+y^2=6x#
using our relationships of conversion.

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How do you convert #r = 6cosθ# into rectangular form?

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