there is an equation I could not figure out. As you see, in the drawing above, there is a shape in polar coordinate. The radius of the disc changes according to the angle.
$\ r(0) = 0 $, and as the angle θ increase, radius r increases as well. But as you noticed, increase of radius has to be in a way that the angle between the tangent of the surface and orthogonal to the center must be always a predetermined constant(Q1).
This is what I've done so far:
$\ r(θ+Δθ) = \frac{r(θ)}{cos(Δθ) - sin(Δθ)cot(Q_1)} $ when $\ Δθ \rightarrow 0 $
I could not achieve to complete the equation and find $\ r(θ) = ? $