Find the Fourier series as far as the third harmonic, to represent the periodic function y, given by the values in the following table.
x
0^{o}
30^{ o}
60^{ o}
90^{ o}
120^{ o}
150^{ o}
180^{ o}
210^{ o}
240^{ o}
270^{ o}
300^{ o}
330^{ o}
360^{o}
y
-3.5
5.1
8.4
8.2
10.3
12.0
9.0
3.4
-6.2
-10.0
-16.5
-14.5
Use a spreadsheet to determine its parameters. Draw the graph of the waveform and explain your working out.