Calculus - Tangent lines and radial lines

[RentonT]

Homework Statement

Let P be any point (except the origin) on the curve r=f(θ). If ψ is the angle between the tangent line at P and the radial line OP, show that

tan(ψ)= (r/(dr/dθ))​

Hint: Observe that ψ = φ - θ in the figure.

Homework Equations

Very few equations come to mind except y = r*sin(θ) and x = r*cos(θ). Also, dr/dθ is equal to f'(θ).

The Attempt at a Solution

See Relevant Equations.

 

[hunt_mat]

Note that:
$$\tan (\psi )=\frac{dy}{dx}$$
In cartesian co-ordinates.