We can see from the graph that f(t + π) = - f(t).

For example, we notice that f(2) = 0.4, approximately. If we now move π units to the right (or about 2 + 3.14 = 5.14), we see that the function value is

f(5.14) = -0.4.

That is, f(t + π) = - f(t).

This same behaviour will occur for any value of t that we choose.

So the Fourier Series will have odd harmonics.

This means that in our Fourier expansion we will only see terms like the following:

a₀/2 + (a₁ cos t + b₁ sin t) + (a₃ cos 3t + b₃ sin 3t) + (a₅ cos 5t + b₅ sin 5t) + ...

[Note: Don't be confused with odd functions and odd harmonics. In this example, we have an even function (since it is symmetrical about the y-axis), but because the function has the property that f(t + π) = - f(t), then we know it has odd harmonics only. The fact that it is an even function does not affect the nature of the harmonics and can be ignored.]