00:01
So in this question, the position of an object in circular motion is modeled by given parametric equations here.
00:07
And it looks like those parametric equations are x equals two times the sign of t and y equals two times the cosine of t.
00:19
We want to describe the path of the object by stating the radius of the circle, the position at time zero, the orientation of the motion, and the time that it completes to complete the time.
00:31
That it takes to complete one revolution around the circle.
00:36
So what i'm going to do here in order to figure out what's happening with this parametric curve is i'm going to make a txy chart.
00:48
And i'm going to choose some t values.
00:51
So i'm going to choose zero, pi over two, pi, three pi over two, and two pi.
01:01
And i'm going to plug in to these parametric equations.
01:06
So let's do the x's first.
01:09
When t is zero, my x will be two times the sign of zero.
01:16
Sign of zero is zero, two times zero, zero.
01:22
When t is pi over two, my x is two sign of pi over two.
01:30
Sign of pi over two is one.
01:33
Two times one is two.
01:37
Then when t is pi is pi.
01:41
My x is 2 times the sign of pi.
01:45
Sign of pi is 0.
01:47
2 times 0 is 0.
01:52
Then when t is 3 pi over 2, my x is 2 sine of 3 pi over 2.
02:00
The sign of 3 pi over 2 is negative 1.
02:04
2 times negative 1 is negative 2.
02:10
And when t is 2 pi, my x is 2 times the sign of 2 pi.
02:18
Sine of 2 pi is 0.
02:21
So my x is 2 times 0, which is 0.
02:26
Now let's get our y's.
02:29
If t is 0, my y is 2 times the cosine of 0...