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Trigonometry - Example 3

Trigonometry is the branch of mathematics concerning the relationships between the sides and the 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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the test. Welcome to our trigonometry Review video on how to plot Trig and metric functions. We've already reviewed the basic I the basic shape of tricking a metric functions, especially for sine and cosine. Remember for sign that it started at 00 and then went back and forth like this. That was for sign. Meanwhile, for cosine, it simply had a different starting point and then the same basic structure. So instead of starting at 00 was started at zero. What? Cool. Okay, What this means is, if we were to plot tangent, I mentioned briefly before that. Remember, Tangent of X is equal to sign of X divided by co sin of X. And because coastlines in the denominator, every time it passes through zero, we're gonna end up with a vertical acid toad. Okay? Which means that tangents gonna look something like this for those two dash marks are indicative of where cosine is equal to zero. Okay? And it will repeat itself just like sine and cosine repeat themselves. Okay, But let's come back to Sine and cosine because really there what composed tangent? They're the most interesting functions that we have to deal with here thinking about sign. First thing we might ask ourselves is Well, we know the amplitude is one and negative one. Ah, the other thing we might ask us. How often does this thing repeat? Um, it's a good question. So it turns out that if we use our new unit that I showed you in the conception in the last video unit of Radiance. Okay, so we're going to use data and radiance. Okay, We plot against it. I have sign of X here, then what we're going to see is that a full period from beginning to end before it repeats itself again is going to be a distance of two pi. Okay, so it's two pi radiance to go around in a full circle. So this is equivalent to 360 degrees. Two pi radiance. Okay, if we wanted to go halfway, that would be pie radiance. If we wanted to go 1/4 of the way that be pi over two, Um so pie then would correspond to 180 degrees, and pi over two would correspond to 90 degrees. And that means that our period is two pi. Now we want to know is there Are there ways to affect these functions? Like there are other functions that we have so say Instead of just sign of X day, we had a function f of X is equal to a time sign of B X plus c. Okay, so we've added in some other variables here A, B and C and A, B and C Here are constants. Okay, A is what we're going to call the amplitude. All it's going to affect is how high and how low does the function go. Remember, Sign has a maximum of one. A minimum of negative one. So by multiplying it by a sign now has a maximum of a and a minimum of negative A. Okay, so now sign will go up to a and down to negative eight. Alright. B and C are a little more complicated. See, um is going to shift it. Remember that we talked about how sine and cosine are slightly different. Well, if I were to put in sign of X plus pi over two, okay, then I would actually end up with a function or a value. That's exactly what sign of exes. So see, here is what's called a phase shift. And if we put in the right face shift, we can end up with the exact same thing for sign of X. As we have for co sign of X, we have sign of X plus pi over two. In this case, um, now be on the other hand, is related to the period. Okay, If we have B, then the period can be changed. It is equal to two pi over B. So as long as B is one, we have a period of two pi t here is a generic variable I'm using for the period. But if we have B is equal to two than the period ends up being pie. If B is less than one than the period will get larger. So you should try putting these into your calculator and playing with it to see how different values of A and B and C affect these functions.

RC
University of North Carolina at Chapel Hill
Top Physics 101 Mechanics Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Zachary M.

Hope College