Question

Give an example of an odd function, other than f(x)=0, for which f(x)=f(x+4π).

...I just found the answer sin(x+4π)=sinx – but it was a random guess, and i cant explain my reasoning... i know that sin is an odd function as sin(-x)= –sin(x) - but thats about it. 

Answer 1

f(x) = f(x+4π) is a periodic function with the period of 4π
Since sinx has a period of 2π, you can write f(x)=f(x+2π) = f(x+4π)...

Another example of odd function : f(x) = tan x