Question

How do you graph `r=2costheta`?

Answer 1

`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]}