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Thread: slope of tangent line to polar curve

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    slope of tangent line to polar curve

    Find the slope of the tangent line to the polar curve for the given value of \theta
    r=1/\theta;        \theta=2
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    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by vinson24 View Post
    Find the slope of the tangent line to the polar curve for the given value of \theta
    r=1/\theta;        \theta=2
     \frac{dy}{dx}=\frac{r'(\theta)\sin\theta+r(\theta)  \cos\theta}{r'(\theta)\cos\theta-r(\theta)\sin\theta}

    So in our case  \frac{dy}{dx}=\frac{-\tfrac{1}{\theta^2}\sin\theta+\tfrac{1}{\theta}\co  s\theta}{-\tfrac{1}{\theta^2}\cos\theta-\tfrac{1}{\theta}\sin\theta}

    So just plug in  \theta=2 to get your answer.
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