Derive expressions for the amplitude An and phase angle n for the triangular wave in Figure 134

Derive expressions for the amplitude An and phase angle ϕn for the triangular wave in Figure 13–4 and write an expression for the first three nonzero terms in the Fourier series with A= π2=8 and T0 =2π=5000 s.

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Waveform Constant (dc) A Fourier Coefficients a=0 all n b=0 all Cosine wave fit) -To- AM Sine wave f(r) AL-To- AM Square wave K(1) A a=0 a = A 4 01 ba=0 all n Q=0 =0 all b = A b=0n 1 4 =0 4-0 all n To- b = nodd b=0 neven Rectangular pulse fin To A AT an=24sin (XT) b=0 all Waveform Fourier Coefficients Sawtooth wave fir) %=0 all in all n To Triangular wave -To- -A 9=0 a = 81 (x) %=0 b=0 nodd even Half-wave rectified sine wave a = fit) 2A/x even 1-2 A-T- Full-wave rectified sine wave =0 odd b =4 a=1 b=0 1 %=2A/x 4A/x 1-2 neven %=0 b=0 odd Parabolic wave =0 Q=0 all n 32A b = nodd (x3 b=0 neven