Understanding the Maclaurin Series for Trigonometric Functions

[nicolette2413]

The question is Find the Macluarian Series for f(x)= cos x. Not a hard problem. What I'm having an issue with is Maclaurian series over all. I don't really understand them and how to use them. Our textbook discussion on it is not very helpful either. Can anyone point me in the right direction for help here?

 

[HallsofIvy]

What do you mean by "use them"? Can you give an example of the kind of thing you feel you do not understand?

 

[Feldoh]

A Maclaurin series is the same as a Taylor series centered about 0. (a = 0, in other words). This means locally, at 0 the series will approximate a function the best, then it becomes a little off if you move away from 0, however this can be fixed by adding more terms to the series.

Basically the practice behind cosine is is that if we add an "infinite" number of terms the Maclaurin series for cosine actually equals cosine. This becomes a very nifty tool for evaluaing some integrals.

 

[nicolette2413]

Ok, that makes sense. So to write the series out in the long form for cosine you start at x=0 and work up from there? (such as to 1, 2, or 3) or do you work up in another manner such as in degrees or in terms of "x" such as x², x³?

 

[Feldoh]

You work in terms of a Taylor series with an infinite number of terms, with all of the terms of the infinite series centered about a=0.