00:01
Okay, we've got a point that starts at 3 .50.
00:06
So let's sketch coordinate grid.
00:10
I'll just do one, two, three, four.
00:14
So here's my point right there at 3 .50.
00:22
And it's gonna move counterclockwise along a circular path.
00:30
The radius is 3 .5.
00:33
So let's get that circular path sketched in.
00:38
So i'll add four unit tick marks to the rest of my axes.
00:48
And then we know we'll go through 0 .3 .5.
00:54
Kind of eyeball it there and it will go through zero, or it'll go through negative 3 .50 and then zero to negative 3 .5, back to where it started.
01:10
Okay, so there's the path that the point will follow.
01:18
An angle with its vertex at the circle's center measures theta radians and subtends the path the point travels.
01:30
Okay, so it's a good thing that this is kind of mirroring standard position where an angle has its initial side on the positive x -axis and its terminal side somewhere in the plane.
01:48
So imagine our point is like here.
01:54
And so it's moved along that path this way.
01:58
And we're just kind of following it with this angle here, which works out to be in standard position.
02:12
Um, x is gonna represent the point's x -coordinate.
02:18
Okay, so it's got some coordinate x, y.
02:23
Okay, so first we need to write an expression in terms of theta to represent the point's distance to the right of the center of the circular path in radii.
02:35
Okay, so our formula is x equals r cosine.
02:46
Theta.
02:48
So in terms of radii, our x -coordinate is cosine theta radii away from that center...