Chapter 10.7, Problem 38AYU

In Problems 35-38, find parametric equations that define the curve shown.

To determine

To find: A parametric equation for the curves defined.

Answer to Problem 38AYU

$x=\text{ cos}\left(\frac{\pi }{2}\left(t-1\right)\right)$ and $y=4\text{sin}\left(\frac{\pi }{2}\left(t-1\right)\right)$, $0\le t\le 2$

Explanation of Solution

Given:

Calculation:

From the graph we see $x$ and $y$ intercepts as $(0,4)$ and $\left(0,-4\right)$.

Let $x=\text{ cos}\left(\frac{\pi }{2}\left(t-1\right)\right)$ and $y=4\text{sin}\left(\frac{\pi }{2}\left(t-1\right)\right)$ such that $0\le t\le 2$.

The parametric equation is,

$x=\text{ cos}\left(\frac{\pi }{2}\left(t-1\right)\right)$ and $y=4\text{sin}\left(\frac{\pi }{2}\left(t-1\right)\right)$, $0\le t\le 2$