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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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### Video Transcript

on the trick function y equals four cosign times too omega, plus 30 degrees minus five. So let's go ahead and start with our horizontal transformation. And we get this where we added that 30. Now, Really, the pattern is should be omega minus negative, 30. So because this is plus, it's a minus and negative, which means it's a negative 30 degrees, which means we're going to shift to the left. Negative. 30. Well, each unit is 45 degrees, so we'll shift each of these over. They won't go a full to the next line, but they'll kind of go almost to it to the lift, so that purple is our horizontal shift. Now let's do our vertical shift. We're gonna get our vertical shift. First thing we're gonna do is we're gonna find our midline, which is negative. Five. I got that from this point right here. So right there is my midline. We need to also use our amplitude to find the amount is going to stretch. So we're gonna use that absolute value of A, which is absolute value of four, which is four. So means we're gonna come up for and we're going to come down for, So when we stretch it, it could go to those lots. So let's stretch it out. Remember that if it's on the zero axis, I'm just gonna go ahead and draw those points on the midline. And then basically, if we're looking at the purple graph, if the purple graph points are on positive one, they're going to come up here to this top dotted line. If their own negative one, they're going to come down to this bottom line, so there will be my horizontal stretch.

Liberty University

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##### Alisa L.

University of Texas at Austin

AH
##### Ahyeon H.

University of California, Berkeley

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor