Parametrization is given for a curve
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# Parametrization is given for a curve

[From: ] [author: ] [Date: 11-05-25] [Hit: ]
Indicate the direction in which the curve is traced.(b) Find a Cartesian equation for the a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?Thanks in advance!-A graphing calculator might help you with these or the link given below.(a) By hand,......
x = cos (t)
y = sin (t)
0 <= t <= pi

(a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced.

(b) Find a Cartesian equation for the a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?

-

(a) By hand, I know, and you probably learned, that
(cos (t))^2 + (sin (t))^2 = 1

so all of this curve is on a circle.

The introduction to trigonometric functions usually has a discussion that tells the this traces the circle counter-clockwise (when x-axis points to right and y-axis points up). The terminal points are given by t=0 and t=pi; I will let you do that.

(b) I pretty much gave you this.

Use the link below and put "plot x = cos (t), y = sin (t), 0 <= t <= pi"
and then "plot x = cos (t), y = sin (t), 0 <= t <= .7*pi"

If you need, use the "pdf" option.
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