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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. Trigonometry is most simply associated with planar right-angle triangles (those that have one right angle). Such triangles are the only ones that have a trigonometric ratio associated with their angles. Historically, trigonometry was also called "trigonomics" (from the Greek ???????? trig?non, "triangle" and ?????? metron, "measure"). The term "sine" (Latin sinus) was coined by the Dutch mathematician Willebrord Snellius (1591–1626) and was derived from the word "semijunctus" (half-divided).

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Lily A.

Johns Hopkins University

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Ahyeon H.

University of California, Berkeley

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University of North Carolina at Chapel Hill

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Oregon State University

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Donald and vertical transformations of, um, trick functions. So now let's look at one that's got multiple means we're going to do both horizontal and vertical. Now, here I've drawn the basic cosign the parent function. So we want to start off with going ahead and finding our horizontal switch. And we do that by finding our h R. H. And this one is pi over three. And because it's positive, we're gonna move it to the right. Now, if it helps and you want to change that two degrees, you would just multiply that by 1 80 over pie, and that would give you 60 degrees. So we're gonna move each of these points 60 degrees over to the right, so that's what it would look like at that horizontal shift. So now let's look at our vertical shift. Now for a vertical shift, we're going to do several things. One, we're gonna find our amplitude and our amplitude, and this one is the absolute value of A which is going to be four. We're going to find our period, and our period is going to bay 300 because we're doing cosign. It's 3 60 divided by absolute value of B. So one half, which is gonna be 720. So that means there is going to be a stretch. So we're not just moving this up or stretching it out and then we're gonna find r K and R. K is negative six. So that means my midline is negative. Six. Since my amplitude is four, I'm gonna do four. I'm gonna use a line for below this midline and four below there. So instead of these points that they are above where it's just the zero positive one and negative one, we're gonna stretch it out where it's gonna go between these lines. So to do this, we're basically we're gonna bring her points down, and if it's on zero, we're gonna put it on the midline. If it's a positive one, we're gonna put it here negative to. And if it's a negative one, it's gonna be a negative 10. So, for example, where we have zero and we're gonna use this blue line, we're not looking at the pink. We're looking the blue because that's our horizontal shift. So we're gonna bring it down for my next blue point. We're gonna bring it because it's that one. We're gonna bring it up to that negative too. My next point is on zero. So we're gonna bring it down to where it's going down the mid line. Next we have one that negative once we're gonna bring it all the way down to negative 10. My next point is on the X axis, so it will be on the midline, and my last point is a positive one. So it will also be on this negative, too. And then I'll draw my degrees. So that is my The blue and the green are the two shifts we've done for this transformation. So when you're doing the transformations, you wanna look and make sure you have a stretch which typically you will. And then you wanna find that amplitude from your midline. So, for example, are amplitude was four. So that means we did. We did four lines above the midline and the four lines below the midline. And so that kind of helps us find our stretch for our final graph.

Liberty University

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No Related Subtopics

Lily A.

Johns Hopkins University

AH
Ahyeon H.

University of California, Berkeley

Boris M.

University of North Carolina at Chapel Hill

Heather Z.

Oregon State University