Answer Happy

Question 1 (Unit 11) - 17 marks Consider the periodic function f(t) with fundamental interval - ≤ t ≤T that is defined by -t-T for - < t < 0, f(t) = -πT for 0 < t < π, f(t + 2π) = f(t). (a) Sketch the graph of the function f for -3 ≤ t ≤ 3, and hence state whether the function is even, odd, or neither even nor odd. (b) Calculate the Fourier series for f(t) and hence show that the first few terms are 3 2 F(t) -³-²-cos(t) cos(3t) 9T 1 - sin(t) + sin(2t)- 2 == sin(3t). [3] [14]