Originally Posted by

**kingwinner** __Riemann-Lebesgue Lemma:__

If g is piecewise continuous on the interval [a,b], then

b

∫ g(t) sin(ωt) dt -> 0 as ω->∞

a

[this is quoted directly from my textbook]

(i) Now assuming this result, is it possible to prove from this result that

b

∫ g(t) cos(ωt) dt -> 0 as ω->∞ ??

a

I think it also works for cosine because cosine is just a horizontal shift of sine, but does this imply that the second result(with cos) is an immediate consequence of the first(with sin)? How can we prove this?