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Thread: 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 $\displaystyle r=cos^3(\theta)$ at the point corresponding to $\displaystyle \theta=\frac{\pi}{4}$

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

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

    I will calculate $\displaystyle \frac{dy}{dx}$ at $\displaystyle \theta=\frac{\pi}{4}$ , 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 :
    $\displaystyle y-y1=m(x-x1)$

    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
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    $\displaystyle r =\cos^3{\theta}$

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

    $\displaystyle y = r\sin{\theta} = \cos^3{\theta} \sin{\theta}
    $

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