00:01
First, i want to verify that this has an initial value of y pi equals 0.
00:09
So we're just going to plug in pi for every t value.
00:13
So negative pi times cosine of pi minus pi.
00:24
And we want this to equal zero.
00:27
So cosine of pi is a quadrantsal angle.
00:31
Pi is located here.
00:32
This is zero.
00:33
So, pi halves, pi, and three pi halves.
00:40
And pi is here.
00:41
This coordinate is negative 1, 0, and that's cosine, sine.
00:46
So cosine in this case is negative 1.
00:48
So we have 0 equals negative pi times negative 1, because cosine of pi is negative 1, all minus pi.
00:56
So 0 equals and a negative times a negative gives us a positive pi, and anything minus itself is 0.
01:03
So this initial condition checks out.
01:08
We also need to verify that it is a solution of this equation here...