Question

Question:

Equations:

My attempt (sorry for uneatness) :

Tutorial questions - Sine and Cosine transforms 9. U se the Fourier Inversion Theorem to prove for a real-valued odd function f(t) that F.(w) sin wt du at points of continuity. (Hint: first simplify the integral expression for F(w).) Fourier Inversion Theorem. At points where f0) is continuous, is that t at t=( iwt extra te Fo F(w)-マ27: J-0,f(t)e-iwt dt = F(f(t)) w) is called the Fourier cosine transform of f(t). Similarly, for a real-valued odd function f(t), at points of continuity f(t),汽10 Fs()sina tda, Fol -@freysinut dt-Fare). sw) sin wt dw, where Fs where t sin wt dt s tto :S Lu) 오2 2 22.

Answer 1

a) from urer nverse Throrm -7.ven) f(t ) İs veed valued. Odd function fw)is also Odd function but with copie Ones fue) -iuot he re fio is odd functien t, fit) ˇ苛. nwtdu