00:01
Howdy once again, so we have the position of an object and circuit of motion modeled by a parametric equations below where x is equal to sine 2t, y is equal to cosine 2t.
00:13
And you'll notice to the right here, we have our parametric equations for the unit circle.
00:23
Now, in the unit circle, we know that our x is cosine x.
00:34
And our y is sine of x.
00:41
And that's going to be a little different here, as we can see.
00:47
And so the first question we want to know is, what is our radius? for one, what we'll notice is that cosine and sine of x give us values from negative one to one.
01:07
And there's no changing that here, right? is sine 2 of t is still just going to give you values negative 1 to 1.
01:14
And y is going to give us values from negative 1 to 1.
01:19
And so we're going to have a little circle with radius 1.
01:28
Because it's going to have a diameter of 2 from negative 1 to 1.
01:32
Therefore, the radius is just going to be 1.
01:37
There is no changes there.
01:42
Is that the full extent of that question? yeah, it's just one.
01:48
And now we're concerned with our position at time zero.
02:00
T equals zero.
02:02
Now we can just solve for that.
02:04
So x equals sine to zero, sine of zero.
02:16
You can check the unit circle since at sine theta zero, that's zero degrees, and sine is y that is equal to zero.
02:29
Likewise, for y, cosine 2 times 0, cosine 0.
02:40
You can check that once again on the unit circle.
02:43
That is equal to 1.
02:45
Therefore, our position at that point is 0 .1.
02:51
You'll notice that that is a little different than the unit circle.
02:55
That's about this point right here, because they're switched.
03:01
And then we want to know the orientation of motion.
03:19
Motion of motion.
03:26
And so we know at t equals zero, that's zero to one.
03:29
We only have to check which direction is going for say t equal to say pi.
03:41
All right, if that's the case, then our x is going to be, and let's do pi over two just because this actually goes substantially faster.
03:52
So our x is going to be sine 2 times pi over 2, which is equal to sine pi.
04:07
And once again, you can check that right here at pi...