Question

Sketch the curve with the given polar equation...?

I recognize it as a rose curve, but I don't know how to do it the way the question's asking.

Answer 1

(see explanation)

...does anyone know how to format a table in Socratic LaTeX?

Explanation:

The period of `2+\sin\color(red)(3)\theta` is `2\pi\div\color(red)(3)=(2\pi)/3`. At `\pi/6n` the graph reaches its highest points, the amplitude of 2 (which is 3 due to the graph being shifted upwards).

From a table of `\theta` with intervals of `\pi/6`, calculating `r`:

Cartesian
Polar