00:05
We want to graph the polar curve r equals theta for theta between negative pi over 2 and pi.
00:15
So here's when theta is negative pi over 2, this angle down here.
00:22
And we're going from negative pi over 2 to theta is 0, theta is pi over 2, and eventually theta is pi.
00:30
All right.
00:32
So when theta is the angle negative pi over two, r equals theta, which is equal to negative pi over two.
00:43
Negative pi over two, let's do some values here, a little table.
00:57
All right, so we're graphing r equals theta as theta moves from negative pi over two radians to pi radiance.
01:08
Now, if r equals data, when data is negative pi over two, r equals negative pi over two.
01:14
But it helps to actually graph it to get an approximate number for this.
01:21
So pi is approximately 3 .14.
01:24
So negative 3 .14 divided by 2 is negative 1 .57.
01:32
So approximately negative 1 .57.
01:36
I won't keep putting in the approximate symbol, but just know these are approximate.
01:42
So negative 3 .14 divided by 4, approximately 0 .79.
01:54
Well, if theta is 0, r is 0.
01:57
If theta is pi over 4, then r is pi over 4, so positive .79.
02:04
This was negative pi over 4, so this was negative .79.
02:08
Pi over 2 is going to be positive 1 .57.
02:13
We know that pi is going to be approximately 3 .14.
02:17
Remember, r equals theta, so whatever theta is, that's what r is.
02:22
3 pi over 4, 3 times 3 .14 divided by 4, approximately 2 .35, about 2 in a third.
02:37
As theta moves through these angles, these will be the r values.
02:42
So let's work with these couple negative.
02:44
Let's work with this zero first.
02:45
When the angle is zero, radiance, r is zero.
02:49
That's this point right here.
02:51
Let's work with some of these negative angles.
02:54
When the angle is negative pi over 2, r is negative 1 .57.
03:01
Since r is negative 1 .57 in this direction, it's going to be positive 1 .57 in this direction...