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Trigonometric and Exponential Functions - Example 8

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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So here you're going to see the value of knowing some common values on the unit circle. So those values that came from the 30 60 90 in the 45 45 90 triangle. Because let's say we want the exact value of cosine squared of Piper eight. Well, Piper eight isn't on my list of common values from the unit circle. So what in the world do I do? Well, notice we can do something kind of silly. I'm going to say CoSine of pi over four is equal to co sign of pi over eight plus pi over eight. Okay, that's great. But I know what goes on a pirate fortress that's square into three. Over to Yeah, that's one over squared of two. Here we go. Okay. Well, how is this helping me at all? Well, I can use the angle edition formula here for Kassian. This is cosine squared pi over eight minus sine squared pi over eight. But okay, I'm looking for cosign squared. Piper eight. I don't know what sine squared Piper it is. But remember, I can also use the Pythagorean identity because negative sine squared. We've already seen This is actually cosine squared plus one. So I have this equation one over square root of two is equal to to co sine squared. However, eight plus e think that's supposed to be minus one? Yeah, because negative sine squared. Let me just This will probably help you to So sine squared, Let's go sine squared equals one. So if I saw for negative sine squared, I should have co sine squared minus one. Yeah, so that should be a negative. So this is minus one. And then I could just solve for because I m squared five rate so I can add one and then divide by two. That one over squared too. Plus one all divided by two. So this is the answer. And now you may ask the question, Why would I ever think to do this? This was a very strange I found what cosine squared pi over eight was by considering cosign power before. Well, I'm not saying that this is something you're going to do all the time, but I think this is a useful snapshot to show you that knowing some of these special values really can't allow you to find other values of different angles.

Georgia Southern University
Top Calculus 1 / AB Educators
Catherine R.

Missouri State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Joseph L.

Boston College