Q 8. - Calculus

Question

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.

$x=\sin h t$, $y=\cos h^{2}t$, $t\in \mathfrak{R}$

Step-by-Step Solution

Answer

The solution is:

Step 1. Given information.

The given parametric equations are:

$x=\sin h t$, $y=\cos h^{2}t$

Step 2. Find the values of x and y .

Substitute different $t=-2,-1,0,1,2$ (assume) values in the parametric equations.

$\left(x,y\right)=\left(\sin h t, \cos h^{2}t\right)$

The tabular representation of the points is as follows:

$t$	-2	-1	0	1	2
$x$	-3.62	-1.17	0	1.17	3.62
$y$	14.13	2.37	1	2.37	14.13

Step 3. Draw the graph of the given parametric equations.

The graphical representation is as follows: