Question

How do you write the equation using rectangular coordinates given `r=costheta`?

Answer 1

`x^2+y^2=x` - This is the equation of a circle with center `(0.5,0)` and radius `0.5`.

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is `x=rcostheta`, `y=rsintheta` and `r^2=x^2+y^2`.

We can use this to convert equation in polar coordinates to an equation with Cartesian coordinates.

As such `r=costhetahArrr^2=rcostheta`

or `x^2+y^2=x`

This is the equation of a circle with center `(0.5,0)` and radius `0.5`.
graph{x^2+y^2=x [-0.667, 1.833, -0.605, 0.645]}