00:01
Sketch the graph of r equals 1 minus sine theta.
00:03
So we're wanting to find the ordered pairs r and theta to put on our polar graph.
00:09
So i would pick, first of all, my values of theta for sign.
00:15
And i would pick the values like 0, 30 degrees, then i would go 90 degrees, then i would go 150 degrees, and i would go 150 degrees, and i would continue this until i get to 300 degrees.
00:30
60 degrees so 180 then we're going to have notice i'm picking the ones where the reference angle is 30 and the reason i'm doing that is because i the we get an easy value for the sign of that angle and then i'm also picking my quadrantal angles so let's start with the quadrental angles that's going to be my zero my 90 degrees 180 degrees, and 360 degrees.
01:06
I know that at 0, that's going to be 1 minus sign of 0, which is going to be 1 minus 0 or 1.
01:15
Then i'm going to go to my 90 degrees.
01:17
Here i know that that's going to be 1 minus sign of 90, which i know that's going to be 1 minus 1 or 0.
01:26
I'm going to go to 180 now.
01:28
1 minus sign of 180.
01:30
It's going to be 1 minus negative 1, which is going to be 2.
01:35
Let's go to 270.
01:37
That's going to be 1 minus sign of 270, which is going to be 1.
01:43
I'm sorry, i made a mistake up here.
01:45
That's going to be 1 minus 0.
01:47
I was ahead of myself.
01:48
1 minus 0, which is 1.
01:50
I knew that didn't look right.
01:52
So let's go and erase that to a 1.
01:58
270 is going to be 1 minus negative 1 or 2.
02:02
And then we go to 0, we're going to have 1 minus sign of 360, which is 1 minus 0 or 1.
02:11
So therefore i know that.
02:12
Now, the other ones we have, the reference angle is going to be 30.
02:17
And i know that the sign of 30 degrees is going to be 1⁄2.
02:24
So we just need to determine whether it's going to be positive 1⁄2 or negative 1⁄2.
02:29
Well, in the first quadrant, let's go and write this out.
02:33
It's going to be 1 minus sign of 30.
02:36
In the first quadrant, that's going to be a positive 1 -half.
02:39
So that's going to be 1 -half.
02:41
In the second quadrant, sign is also positive.
02:45
So that's also going to be a positive 1 -half.
02:50
In the 3rd and 4th quadrant, sign is negative.
02:54
So that's going to be 1 -1 -6 of 2 -10, which is going to be 1 -9 -1 -5, or 1 -1 -5.
03:03
And it'll be the same thing for 330.
03:07
That'll be 1 minus sign of 3 .30, which will be 1 minus negative 1 .5, or 1 .5.
03:16
Got a lot of points here...