Chapter 10.7, Problem 44AYU

In Problems 43 and 44, the parametric equations of four curves are given. Graph each of them, indicating the orientation.

$C_1:x=t,y=\sqrt{1-t^2};-1\le t\le 1$

$C_2:x=\sin t,y=\cos t;0\le t\le 2\pi$

$C_3:x=\cos t,y=\sin t;0\le t\le 2\pi$

$C_4:x=\sqrt{1-t^2},y=t;-1\le t\le 1$

To determine

To graph: The four curves defined by the given parametric equations.

Answer to Problem 44AYU

a.

Explanation of Solution

Given:

$C_1:x=t,y=\sqrt{1-t²};-1\le t\le 1$

Graph:

The graph of $C_1:x=t,y=\sqrt{1-t²};-1\le t\le 1$ is plotted.

To determine

To graph: The four curves defined by the given parametric equations.

Answer to Problem 44AYU

b.

Explanation of Solution

Given:

$C_2:x=\text{ sin}t,y=\text{ cos}t;0\le t\le 2\pi$

Graph:

The graph of $C_2:x=\text{ sin}t,y=\text{ cos}t;0\le t\le 2\pi$.

To determine

To graph: The four curves defined by the given parametric equations.

Answer to Problem 44AYU

c.

Explanation of Solution

Given:

$C_3:x=\text{ cos} t,y=\sin t,0\le t\le 2\pi$

Graph:

The graph of $C_3:x=\text{ cos} t,y=\sin t,0\le t\le 2\pi$.

To determine

To graph: The four curves defined by the given parametric equations.

Answer to Problem 44AYU

d.

Explanation of Solution

Given:

$C_4:x=\sqrt{(1-t²)},y=t,-1\le t\le 1$

Graph:

The graph of $C_4:x=\sqrt{(1-t²)},y=t,-1\le t\le 1$.

The graphs of $C_1:x=t,y=\sqrt{1-t²};-1\le t\le 1$.

$C_2:x=\text{ sin}t,y=\text{ cos}t;0\le t\le 2\pi$

$C_3:x=\text{ cos} t,y=\sin t,0\le t\le 2\pi$

$C_4:x=\sqrt{(1-t²)},y=t,-1\le t\le 1$ are plotted and the orientations are also shown.