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Question

# The parametric curve x = 2 cos (-t), y = 2 sin (-t),0 ≤ t ≤ 2π is traced clockwise. Justify your answer.

Solution

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We list a few coordinates for $(x,y)$ in the given interval:

$\def\arraystretch{1.5} \begin{array}{cc} \boldsymbol{t} & \boldsymbol{(x,y)}\\\hline 0 & (2, 0)\\ \frac\pi4 & \left(\sqrt2, -\sqrt2\,\right)\\ \frac\pi2 & \left(0, -2\right) \end{array}$

From the coordinates we see that the curve is traced clockwise. The statement is \textcolor[RGB]{120,0,0}{true}.

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