What is this trigonometric graph?

Question

I polar graphed $r=\sin(1.31459x)$ instead of $r=\sin(1.31459\theta)$, which uses the variable $x$ instead of $\theta$. Mac Grapher provides the result pictured below. I'm confused because $x$ should not be a variable in a polar graph, yet here is the result.

Question 1 Does anyone know what I actually graphed and why it worked with the variable $x$ instead of $\theta$?

Graph $r = \sin(1.31459x)$:

Answer 1

You may use polar co-ordinates $(r,t)$ $x=r\cos t, y=r \sin t$ and use ContourPlot of Mathematica for $\sqrt{x^2+y^2}=\sin(\pi x),x\in(0,1), y\in(-1,1).$

Answer 2

Grapher is automatically converting $x$ into $r cos \theta$. The polar form is $r = sin(k r cos(\theta))$, where $k = \frac {\pi} {10} + 1$. The Cartesian form is $\sqrt {x^2 + y^2} = sin(kx)$.