Find Exact Trigonometry Functionsof Angles
In mathematics, a trigonometric function is a function of an angle. The function values are related to the angles by trigonometric identities. The most familiar trigonometric functions are the sine, cosine, tangent, and their inverses.
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Alisa L.
University of Texas at Austin
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University of North Carolina at Chapel Hill
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Michigan State University
Kristen K.
University of Michigan - Ann Arbor
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exact Trig values of angles in A you're from a unit circle. In order to do this, we're gonna use a couple different things. First thing we're gonna do is a periodic function, and a periodic function says if I've got a sign of cosign measurement, um, with degrees, like 23 60 and radiance will have, that's two pi, and that's how we'll get our measurement. So once we find that we're gonna use this unit circle right here, you can look this up on Google. If you can't have, don't have your own copy. A lot of them are in textbooks that will give us exact degrees of angles. So let's look at one and looks like at cosign of 675 degrees now for this 1 675 is greater than 360 we're needing to find that measurement between zero and 3 60. So what we're saying is that hey, cosign off 6. 75 came from some number plus 360 degrees. Well, the way we find that out is we subtract 6 75 minus 3 60 and that gives me 350 So this tells me that we're looking for the co sign of 675 degrees equals 315 degrees plus 360 degrees. So we're looking for the cosign of 315 degrees. So when I can't do that, I come over to my circle and I noticed right here is about 315 degrees. And remember that when you're talking about those X Y coordinates, your cosign is your X coordinate and your son is your Why. So That means that my co sign, a 315 degrees, is the square root of 2/2. Now it is important to understand that 315 degrees is a co terminal angle off 675. So that's why 315 is the exact degrees off about 315 degrees and 675. So let's look at another one. Let's look at sign off negative five pa over six. Now, because this one is negative, we can add that to two pi to find what are exact one is so we're gonna add negative five pi over 62 two pi and I'm gonna go ahead and put two pi over one. Of course, we've got to find that common denominator, and that's going to be six. So we'll have negative five pi over six plus 12 pi over six. Negative five plus 12 is going to equal seven pi over six. So this is what we're looking for to find that exact measurement. So let's have a look at our circle. So we're looking at seven Pi over six, and I notice it's right here. It's a little dark. Let me lighten it up. Just see that better. Okay, so that's 200. It's the same as 210 degrees. So again, we're looking for sign. And when we're looking for signing that X Y coordinate, Kossan is our X coordinate and sign is R Y coordinate. So this means that for this one, we're looking at that Y coordinate, and that equals negative one half
Algebra 2
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Top Algebra 2 Educators
Alisa L.
University of Texas at Austin
Boris M.
University of North Carolina at Chapel Hill
Martha R.
Michigan State University
Kristen K.
University of Michigan - Ann Arbor
