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Math Help - [SOLVED] Slope of a tangent line

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    [SOLVED] Slope of a tangent line

    I have been working on this for a week with no luck. Thanks in advance for the help!
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  2. #2
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    Follow the hint and write the general point on the curve as (\cos\theta,\sin\theta,h(\cos\theta,\sin\theta)), where h(\cos\theta,\sin\theta) = 4\cos^3\theta\sin\theta - 4\sin^3\theta\cos\theta+1. Using a bit of trigonometry, you can simplify that to h(\cos\theta,\sin\theta) = \sin(4\theta)+1, so that the point on the curve is (\cos\theta,\sin\theta,\sin(4\theta)+1). Differentiate this (with respect to θ) to find the direction of the tangent at that point.
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