- #1

Marcus95

- 50

- 2

## Homework Statement

Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ##

What can be said about the coefficients ##a_n## and ##b_n## in the following cases?

a) f(x) = f(-x)

b) f(x) = - f(-x)

c) f(x) = f(π/2+x)

d) f(x) = f(π/2-x)

e) f(x) = f(2x)

f) f(x) = f(-x) = f(π/2-x)

## Homework Equations

Sine is odd and cosine is even. Even functions can only contain cosine terms and odd functions only sine terms in their Fourier Series.

## The Attempt at a Solution

Here is how far I have gotten:

a) All b=0 because even function

b) All a=0 because odd function

c) Funtion has period π/2 (?)

d) Funtion has period π/2-2x (?)

e) Function has period x (not neccessarily the shortest period)

f) All b=0 because even function.

But here I am stuck, because I have no idea how to relate the coefficients to the period in c)-f), and in c)-e) I don't know if the funtion is odd or even.

Many thanks for any help! :)