00:01
In this question, we want to find a parameterization for the curve.
00:04
Here i have a circle of radius 3 centered on the z -axis and lying in the plane z equals 5.
00:12
So we're going to need x, y, and z, each as functions of t.
00:20
Now they tell us this time that we are in the plane z equals 5, so that is going to be z equals 5 as a constant.
00:30
Now i have this circle of radius 3 centered on the z -axis.
00:38
So you may remember that if you have just a unit circle in terms of x and y, how is that parameterized? that is parameterized as x equals the cosine of t and y equals the sine of t for t values from 0 to 2 pi.
01:00
And so now i need this to have a radius of 3.
01:04
My unit circle has a radius of 1, so i need to multiply by 3 in order to get the correct radius.
01:14
So in other words, i'm going to have x equals not 1 cosine of t, but x equals 3 cosine of t...