How do you graph #r=2costheta#?

1 Answer
Nov 12, 2016

#x^2+y^2=2x#

Explanation:

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#

Hence, #r=2costhetahArrr^2=2rcostheta# or #x^2+y^2=2x#

i.e. #(x^2-2x+1+(y-0)^2=1#

or #(x-1)^2+(y-0)^2=1#

which is nothing but a circle with center at #(1,0)# and radius #1#, whose graph is as follows:
graph{x^2+y^2=2x [-1.74, 3.26, -1.27, 1.23]}