(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

I'm new to this site, I've had a look around and there are alot of useful sections, particularly the section with math and science learning materials.

Anyway, I need to show that the following function is odd

[tex]f(x)=\left\{\begin{array}{ccc}

-\sin x&\mbox{ for }-\pi \leq x< \frac{-\pi}{ 2}\\

\sin x &\mbox{ for } \frac{-\pi}{2} \leq x \leq \frac{\pi}{2}\\

-\sin x &\mbox{ for } \frac{\pi}{2}<x<\frac{\pi}{2}

\end{array}\right.[/tex]

[tex]\mbox{ and }f(x + 2 \pi) = f(x) \mbox{

for all other values of x, is an odd function.}[/tex]

2. Relevant equations

I know an odd function is definded as [tex] f(-x) = -f(x)[/tex]

3. The attempt at a solution

In the interval

[tex]-\pi\leq x < {-\pi \over 2} \mbox{ if I substiture } -\pi \mbox{ it becomes }-\sin(-x) = -\sin[-(-{\pi \over 2})] = -\sin({\pi \over 2})[/tex]

Is that the correct way to solve it?

But I'm not sure how to show it's odd in the other intervals!

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# How to show a function is even/odd

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