Question

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x={\sin }^{2}t,y={\cos }^{2}t;0\le t\le 2\mathrm{\pi }.$

Short answer

The equation is$x+y=1$.

Step-by-step solution

Step 1. Given information.

$x={\sin }^{2}t,y={\cos }^{2}t$is given.

Step 2. Form the graph and equation.

we form the rectangular equation by eliminating t in the equation-

$$\begin{gathered} x={\sin }^{2}t \\ y={\cos }^{2}t \\ {\sin }^{2}t+{\cos }^{2}t=1 \\ x+y=1 \end{gathered}$$

Graph the curve defined by the parametric equations -

$t$	$x$	$y$	$(x,y)$
$0$	$0$	$1$	$(0,1)$
$\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$	$1$	$0$	$(1,0)$
$\mathrm{\pi }$	$0$	$1$	$(0,1)$
$2\mathrm{\pi }$	$0$	$1$	$(0,1)$