Calculating the Taylor Series for cos(x) in Powers of x-pi | Homework Help

[TheRedDevil18]

Homework Statement

Find the taylor series representation for the following function
f(x) = cos(x) in powers of x-pi

Homework Equations

The Attempt at a Solution

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I don't know what they mean by "in powers of x-pi", that's the part I'm confused with. Can somebody please explain that part for me, thanks

 

[ShayanJ]

That just means you should expand around x=\pi rather than the usual x=0.

 

[TheRedDevil18]

That just means you should expand around x=\pi rather than the usual x=0.

Does that mean the "a" value is pi ?

 

[ShayanJ]

Does that mean the "a" value is pi ?

If you write f(a+\delta)=\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!} \delta^n, then yes!

 

[TheRedDevil18]

I use this formula

f^(n)(a)*((x-a)^n)/n!

And sub in pi for a, thanks

 

[Mark44]

I use this formula

f^(n)(a)*((x-a)^n)/n!

And sub in pi for a, thanks

Yes, this is what the general term in your Taylor series will look like. Note that a Maclaurin series is a special case of a Taylor series, where a = 0.

 

[TheRedDevil18]

Ok , thanks