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# 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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AH
##### Ahyeon H.

University of California, Berkeley ##### Martha R.

Michigan State University ##### Heather Z.

Oregon State University

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questions on the trick function y equals three signed times one third omega minus pie or two plus two. Now I've already gone drawn our parents graph. So this is a sign. This is just the basic sign graph. So let's start off and let's do our horizontal shift. Ah, horizontal shift is we're going to get from where we've subtracted that pi over two. It is positive. So this means we're going to go to the right, and if it helps, you can go ahead and you can move it. You can change it to degrees if you need to, and that would be 90 degrees now. Each unit is 45. So that kind of tells you. Basically, I'm moving the dots over two units. So here I am, just moving them all over two units. And if I wanted to even do one right there could so there's my horizontal shift. So we're gonna be using this purple line to kind of help us with our vertical shift. Now for a vertical shift. We're looking for a couple of things. One, we're looking for a midline. We're gonna get that from our K, which is positive too so I'm gonna go ahead and draw our midline. This is now gonna kind of almost represent the new X axis among ground. The next thing we're gonna look for is our amplitude. And that's gonna be the absolute value of eight, which in this case, is the absolute value of three, which is three. So that means that we're gonna stretch this out 23 lines above our midline and three lines below our midline, and then we're gonna find we are gonna be stretching out. And I know that because we have a period of one third. So let's go ahead and let's do this. I'm gonna do a different color so we can see this. Well, so are vertical shift. Basically, we're gonna look at this purple wide, and we're going to shift everything up. So the ones that are at negative one, we're gonna actually leave them at negative one, and we're gonna stretch everything else up. So if it's on, the X axis is going to go on the bed line so I can go ahead and draw bows, And if it's on the one, we're gonna bring it up here to these points and then like so if it's some negative one, it's gonna be right there. So right here is going to be the green is going to be my new graph. Liberty University

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AH
##### Ahyeon H.

University of California, Berkeley ##### Martha R.

Michigan State University ##### Heather Z.

Oregon State University