# Thread: Tangent Line on a Parametric Curve

1. ## 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.

2. 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 $T(t)=r\left(\frac{2\pi}{9}\right)+\lambda\left(\co s 3t,-\sin 3t\right),\lambda\in\mathbb{R}$