On a sheet of paper, graph the parametric equation after eliminating the parameter $t$ ( $0 \leq t \leq 2 \pi$ ). Specify the approximate direction on the curve corresponding to increasing values of $t$ . $x = \cos t , y = 2 \sin t$
A) clockwise
B) counterclockwise

Question

Quizplus · Accepted Answer

To eliminate the parameter $t$, we can square both equations and get $x^2+\dfrac{y^2}{4}=1$, which is the equation of an ellipse centered at the origin with semi-axes $a=1$ and $b=2$.

Since the equation is an ellipse, we know that as $t$ increases, the point moves counterclockwise around the origin, tracing out the ellipse in that direction. Therefore, the approximate direction on the curve corresponding to increasing values of $t$ is counterclockwise, so the answer is B.

On a Sheet of Paper, Graph the Parametric Equation After ttt

On a Sheet of Paper, Graph the Parametric Equation After $t$