Chapter 8.4, Problem 38E

To determine

To draw: the curve given by the parametric equations.

Answer to Problem 38E

  

Explanation of Solution

Given: $x=\sin t,y=\sin 2t$

Calculation:

Sketch the curve given by parametric equation $x=\sin t$ and $y=\sin 2t$

To draw the graph, put various values of $t$ and find the corresponding values of $x$ and $y$ .

On tabulating the results,

$t$	$0$	${30}^{\circ }$	${45}^{\circ }$	${60}^{\circ }$	${90}^{\circ }$	${120}^{\circ }$	${150}^{\circ }$	${180}^{\circ }$	${270}^{\circ }$	${360}^{\circ }$
$x$	$0$	$0.5$	$0.707$	$0.866$	$1$	$0.866$	$0.5$	$0$	$-1$	$0$
$y$	$0$	$0.866$	$1$	$0.866$	$0$	$-0.866$	$-0.866$	$0$	$0$	$0$

Using the table, get the following graph of the parametric equations $x=\sin t$ and $y=\sin 2t$ .

  

Conclusion:

Thus, the required curve is drawn.