Wednesday, November 23, 2011

Round and Round – trig functions

Last week we talked about some basic functions that you will deal with in algebra, calculus and beyond. Today I am going to introduce you to some basic trig functions.

One of the most fascinating applications of trig functions is that of daylight hours. Do you notice how the days get longer in the summer, then shorter in the winter? And then they get longer and shorter and longer and shorter, and the cycle just keeps going on.

Trig functions are just that – cycles.

This is a graph of the function f(x) = sin(x) (the one on the left is one period of the sine function, and the one on the right shows more what the graph does – it just keeps going over and over again – in a cycle.)



This is a graph of the function f(x) = cos(x). Cosine is a lot like sine – it just starts in a different place. Where sine starts at zero when x = 0, cosine starts at 1 when x = 0.

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This is a graph of the function f(x) = tan(x). Tangent is a ratio of sine and cosine. The reason it is undefined at some places (see how the graph goes up and doesn’t come back down, and then it stars from far below?) is because sometimes cosine is zero, and you can’t divide by zero.

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This is just a little introduction to show you what trig functions look like. There are also inverse trig functions, which we’ll talk about later. We’ll also talk about some really interesting applications of trig functions.

If you have questions, you can ask them in the comments, email me, ask on Facebook, or on Twitter. I am on Facebook and Twitter live from 3:00-3:30 pm Mon-Thurs MDT.

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