Why does $r=\cos(0.01\cdot\theta)$ show a spiral curve graph?

Question

On WolframAlpha the equation $r=\cos(0.01\cdot\theta)$ shows a spiral graph, but this doesn't make algebraic sense to me. Wouldn't $r$ only have one value for theta?

Answer 1

The values $\theta=0,2\pi$ both look like they are at the same place on the plot. But $r(0)=\cos(0.01\cdot0)=1$, and $r(2\pi)=\cos(0.01\cdot2\pi)=\cos(\pi/50)\approx0.998\neq1$. Similarly, $4\pi,6\pi,...$ all would yield different values for $r$, since $\cos x$ is $2\pi$ periodic, so $\cos0.01 x$ is $200\pi$ periodic, hence you'd appear to get $100$ different values of $r$ along the same line.

Answer 2

The Alpha graph you link to has $\sin$ instead of $\cos$ but the result is similar. It plots $r$ for a range of $\theta$ values. If you asked it to plot $y=0.01 \sin x$ you would not get just one point, you would get a curve that represented a range of $(x,y)$ points.