Sketch the curve represented by the parametric equations .

Question

Sketch the curve represented by the parametric equations  . ​

Quizplus · Accepted Answer

To sketch the curve given by parametric equations, we can find a few points by plugging in different values of t and plotting the corresponding points.

For the given set of parametric equations, x = sin(t), y = sin(2t), we can start by listing a few points:

t | x = sin(t) | y = sin(2t) 
---|-----------|----------- 
0 | 0 | 0 
π/4 | 0.707 | 0.866 
π/2 | 1 | 0 
3π/4 | 0.707 | -0.866 
π | 0 | 0

Plotting these points, we can see that they form a shape that resembles a "butterfly":

![Butterfly Curve](https://www.mathsisfun.com/geometry/images/butterfly-1.gif)

Out of the given answer choices, only choice D has a shape that resembles a butterfly curve.

Sketch the Curve Represented by the Parametric Equations