Homework Help: Calculus - Tangent lines and radial lines

1. Jul 28, 2010

RentonT

1. The problem statement, all variables and given/known data
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.
2. Relevant 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).

3. The attempt at a solution
See Relevant Equations.

2. Jul 28, 2010

hunt_mat

Re: Tan(Psi)

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