mathematics

The plane curve is given by the equation R(t)= ( ln sin t)i + ( ln cos t)j.
find the unit normal vector to the curve t= ¤Ð/6.

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  1. assuming you meant t=π/6

    The unit tangent vector
    T(t) = r'/|r'| =

    cot(t) i - tan(t) j
    -------------------------
    tan^2(t) + cot^2(t)

    The unit normal is T'/|T'| =

    -(csc^2(t) i + sec^2(t) j)
    ----------------------------------
    csc^4(t) + sec^4(t)

    which at t = π/6 is

    -(4i + 4/3 j)/(16 + 16/9)
    = -4/3 (3i+j) * 9/156
    = 1/13 (3i+j)

    as always, check my math

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    posted by Steve

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