Angle of Tangent to Radius in Polar Coordinates

Theorem
Let $C$ be a curve embedded in a plane defined by polar coordinates.

Let $P$ be the point at $\polar {r, \theta}$.

Then the angle $\psi$ made by the tangent to $C$ at $P$ with the radial coordinate is given by:
 * $\tan \psi = r \dfrac {\d \theta} {\d r}$

Proof

 * TangentToRadiusPolar.png