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Math Help - Equation of tangent line (rec. form) to a polar curve!!

  1. #1
    Member Miss's Avatar
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    Equation of tangent line (rec. form) to a polar curve!!

    Hello
    Quesiton:
    Find the rectangular form of the equation of the tangent line to the polar curve r=cos^3(\theta) at the point corresponding to \theta=\frac{\pi}{4}

    How to do that?
    I mean finding it in RECTANGULAR FORM !

    i know that \frac{dy}{dx}=\frac{\frac{dr}{d\theta} sin(\theta)+rcos(\theta)}{\frac{dr}{d\theta} cos(\theta) - r sin(\theta)}

    I will calculate \frac{dy}{dx} at \theta=\frac{\pi}{4} , and this is easy ..
    The problem here is that, how can I find the equation of the tangent line in RECATNGULAR FORM ??

    The equation of the tangent line is :
    y-y1=m(x-x1)

    m = the slope , and this one will be calculated by using the formula ..
    but what about x1 and y1?
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    r =\cos^3{\theta}

    x = r\cos{\theta} = \cos^4{\theta}

    y = r\sin{\theta} = \cos^3{\theta} \sin{\theta}<br />

    sub in \frac{\pi}{4} for \theta to determine x and y
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