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Graph Multiple Transformationsof Trigonometry Functions - Example 2

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Trigonometry is also the foundation of surveying.

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Algebra 2

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multiple transformations to the graph y equals two thirds cosign times one half omega plus, uh, pi over six, minus two. So I've already gone ahead and I've drawn are parent cosign function. So let's do our horizontal now horizontal, even though it says plus past six, remember, that's always gonna be minus a negative pi over six. So we really have a negative pi over six, which means we're gonna be moving this to the left. Now, just if you're gonna change your degrees, go ahead. So that's gonna be we're gonna multiply that but of 1 80 over pie, which means it's negative 30 degrees. This means we're going to do a left shift with all of them negative 30 degrees. So since each unit is 45 it's gonna be kind of in between each point, So it's a pretty close horizontal shift, and that's absolutely fine. So now let's look at our vertical shift are vertical shift. First of all, we can go ahead and do my midline, and that's gonna be negative too. Remember, this is basically gonna be kind of like our new X axis. We are gonna have a stretch on this, but Let's go ahead and find our amplitude are amplitude we get from the absolute value of A, which is in this case, two thirds. So the absolute value of two thirds is two thirds. So this means that we need to kind of come up two thirds on this graph, So that means that it's not exactly going to be right on the next line. It's just gonna be kind of just barely above it, are below it. So this one is going to actually be a very it's gonna be stretched are, But it's not gonna be very, very much so. I'm gonna go ahead and I'm gonna do this vertical shift. So everything that's on the zero Well, actually, we're gonna use this purple would it's going to come onto the midline, so I'm gonna go ahead and do those points first, and then we're going to go ahead. And if it's on, the one is gonna be on this dotted line. And so right here is my vertical shift

Liberty University
Algebra 2

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