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Math Help - Tangent Line on a Parametric Curve

  1. #1
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    Tangent Line on a Parametric Curve

    I'm really confused about this problem: A curve is defined parametrically by x=sin 3t, y=cos 3t, 0≤ t ≤ 2 ∏. Find the equation of the line tangent to the curve at the point defined by t=2 ∏/9. Could you help me? Thanks.
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  2. #2
    Member Abu-Khalil's Avatar
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    Let r(t)=\left(\sin 3t,\cos 3t\right)\Rightarrow \dot r(t)=\left(3\cos 3t,-3\sin 3t\right). Hence, the tangent line is given by T(t)=r\left(\frac{2\pi}{9}\right)+\lambda\left(\co  s 3t,-\sin 3t\right),\lambda\in\mathbb{R}
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