First, we need to define the function:

We can see from the graph that it is periodic, with period 2π.
So f(t) = f(t + 2π).

Also, L = π.

We can also see that it is an odd function, so we know a₀ = 0 and a_n = 0. So we will only need to find b_n.

Since L = π, the necessary formulae become:

Now

We could write this as:

So the Fourier series for our odd function is given by:

NOTE: Since b_n is non-zero for n odd, we must also have odd multiples of t within the sine expression (the even ones are multiplied by 0, so will be 0).

Checking, we take the first 5 terms:

We see that the graph of the first 5 terms is certainly approaching the shape of the graph that was in the question. We can be confident we have the correct answer.