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Calculus - Tangent lines and radial lines

  1. Jul 28, 2010 #1
    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. jcsd
  3. Jul 28, 2010 #2


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    Homework Helper

    Re: Tan(Psi)

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