About this video
The video plots four points given in polar form (r, theta), with angles in degrees or radians. It handles angles bigger than one full turn, negative angles (measured clockwise) and negative radii (go the opposite way along the angle's line).
You'll be able to
- plot a polar point by finding the angle first and then moving out the radius.
- rewrite angles over 360 degrees or negative angles as an equivalent angle between 0 and a full turn.
- plot a point with a negative radius by moving backwards through the origin.
Key words
- polar coordinates
- A way to locate a point with a distance from the origin (r) and an angle (theta) from the positive x-axis.
- radius (r)
- How far to move from the origin along the angle's direction; if negative, move the opposite way.
- radian
- An angle unit where pi radians equals 180 degrees.
- revolution
- One full turn: 360 degrees or 2pi radians.
Transcript
- [Instructor] What we're gonna do in this video is get some practice graphing in polar coordinates. So I have three points here, and some of them are given in degrees. Some of them are given in radians for the angle. And we're gonna think about how to plot it out on these axes, or I guess you could say this graph paper here.
And if you don't have any graph paper in front of you, I encourage you to at least pause the video before I plot it, and at least point your finger on your screen to where you think I should plot it. Alright, let's start with this first point: 3, 405 degrees. So 405 degrees is interesting, because that's more than one full circle around, one revolution.
405 degrees is going to be equal to 360 degrees plus 45 degrees. So we're going to go all the way around, that's going to be 360, and then another 45, which would get us right to that little gray line right over there. And then the radius is 3, so we're going to go 1, 2, 3.
So that is our point, 3, comma, 405 degrees. Now our next one is in radians. And this one's interesting, 'cause the radius is negative. So I like to start with the angle as always. So 3 pi over 4 radians. So if this is pi over 2, this is pi radians, we're going to be exactly halfway in between on this gray line right over here.
But if our radius was 2, we would go out 1,2, but our radius isn't 2 it's -2, so we go backwards. We go 1, 2 right over there. Alright, now, 4, comma, -4 pi over 3. So let's think about where that would be. So here we're in radians, and we have a negative angle.
So we're going to go clockwise, -4 pi over 3. So I always just like to think about, that's, 4 pi over 3 is equal to 3 pi over 3 + pi over 3. So it equals pi + pi over 3. And we're going to, and if we did put a negative here, we would say that. And so let us now go negative pi.
That would take us over here. And then we'd wanna go another negative pi over 3. And my brain sometimes converts back and forth between radians and degrees. I remind myself, well pi is 180 degrees. Pi over 3 is 60 degrees. So that would get us, if we go another negative pi over 3, we would get right over here to 2 pi over 3.
And another way to think about this, if you just took 2 pi at, which is, you could use, this is zero radians or two pi radians, you subtracted 4 pi over 3. Let me do that over here. So 2 pi minus 4 pi over 3, that's the same thing as 6 pi over 3 - 4 pi over 3, which is equal to 2 pi over 3.
And so that gets us to this angle right over here. And our radius is 1, 2, 3, 4. There we go. And then last but not least, we have both a negative angle and a negative radius. This should be fun. All right, let's do the angle first. So -100 degrees, if we view this as 0 degrees, but it could also be viewed as 360 degrees if you made one full revolution, you're gonna subtract 100 degrees from that.
So if you subtract 100 degrees from that, that would be the same thing as 260 degrees. So we get to this angle right over here, and if it was +3, we would go 1, 1, 2, 3, but it's not, it's -3. And let me make sure I'm following this properly. So if I follow this line backwards, I get to that line right over there.
And so I'm going to go backwards, 1, 2, 3, and get to that point right over there, and we're done.
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