00:01
So in this problem, we're given these two equations with different shifts and adjustments in them.
00:09
First one's cosine, the second one's in sine.
00:12
And we're asked to graph these and describe each of the transformations.
00:25
Okay.
00:26
So let's talk about what each of these transformations look like, first of all.
00:30
So if i have y equals a sign of bx plus c plus d, or y equals a cosine bx plus c plus d, either one works.
00:58
Okay.
00:59
Well, a is the amplitude.
01:07
What does that mean? well, in each one of these, this is sine, or no, this is, sorry, this is cosine, and this is sign, and this is sign.
01:34
Then this distance here is the amplitude, how far off of the center it is.
01:47
And the base ones all have the amplitude equal to one.
01:54
Okay.
01:56
B then works with the period.
02:00
And the period is 2 pi over b.
02:06
So if you give me b, the number in front of x there, in front of the input, then i can tell you the period.
02:12
Well, the period is from peak to peak.
02:18
This is the period.
02:22
And so i'll go from here to here, right? as a period.
02:29
Those are from the same point to the same point in one whole cycle.
02:34
Okay.
02:35
Then c is what we call the phase shift.
02:44
Negative goes to the right.
02:48
Positive goes to the left.
02:51
And d is the vertical shift or down.
03:03
Up being positive, down being negative.
03:07
Okay.
03:09
So with that, let's talk about the graph here.
03:15
So i'm in the cosine graph for this first one.
03:18
Which is my base graph looks like this, doesn't it? so my base graph looks like this.
03:32
I'm going to draw this a little bit differently here...