Question

How do you graph `r=3+3costheta` on a graphing utility?

Answer 1

Convert to rectangular form:

`x^2+y^2=3sqrt(x^2+y^2)+x`

Explanation:

Given:

`r = 3+3cos theta`

Convert from polar to rectangular coordinates using:

`r = sqrt(x^2+y^2)`

`x = r cos theta`

So multiplying the given equation by `r` we find:

`x^2+y^2 = r^2 = 3r+3r cos theta = 3sqrt(x^2+y^2) + x`

So we can put the equation:

`x^2+y^2=3sqrt(x^2+y^2)+x`

into our graphing utility to get:

graph{x^2+y^2=3sqrt(x^2+y^2)+x [-10, 10, -5, 5]}

Note carefully that this is not a circle.