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?
Thanks in advance!
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?
Thanks in advance!

A graphing calculator might help you with these or the link given below.
(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 counterclockwise (when xaxis points to right and yaxis 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.
(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 counterclockwise (when xaxis points to right and yaxis 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.