00:01
Alright, in this video, we need to plot these cylindrical coordinates, and then we need to convert them to rectangular.
00:11
So our first cylindrical coordinate, recall that it's in the form r, theta, z for each of these.
00:22
So to plot 5 pi over 2, 2, again, this is my x, this is my y, and this is my z.
00:30
So if r is 5 and theta is pi over 2, again, we're imagining we're facing down in the x, y plane.
00:38
So we're going to, you know, go out a distance of 5 from the origin, rotate pi over 2, which brings us to the positive y axis.
00:48
So it brings us 1, 2, 3, 4, 5.
00:50
It brings us right here.
00:51
I'll just put that lightly.
00:55
So it's as though you're on this quarter circle.
00:59
You've rotated pi over pi over 2, but then we have to.
01:04
Now go up to so i'll plot this in red our z coordinate is two so i'm going to go up from here to so there's our point let's call it p or something there's p and now let's convert it to rectangular coordinates so that's easy to do our x coordinate is going to be our cosine theta which would be 5 cosine of pi over 2 and y is 5 sine theta 5 sine 5 of pi over 2 so that's going to be 0.
01:37
Because cosine of pi over 2 is 0.
01:40
This is 5 times 1.
01:41
So x, y, z would be 0, 5, and then our z coordinate, of course, was a 2.
01:54
Okay, let's do this next one.
01:57
Let's call this point q, that way i can label it.
02:07
All right, so i'm going on a distance of 6...