00:01
So in this question, we want to find the slope of the tangent line to the parametric curve.
00:05
X equals 2 cosine of t, y equals 4 sine of t, at the point, i believe this is pi over 3, it just didn't cut and paste well.
00:16
So if i want to find a slope of a tangent line, that means i need d, y, d x, my change in y over my change in x.
00:26
Now, how do i find d, y, d, x for a parameter curve? well, i take the derivative of y with respect to t, and i divide that by the derivative of x with respect to t.
00:44
What's my derivative of y with respect to t? y equals 4 sine of t, so the derivative of y with respect to t is 4 cosine of t.
00:57
How about my derivative of x with respect to t? x equals 2 cosine of t.
01:04
So my derivative of x with respect to t is negative 2, sine of t...