Expressing a function in terms of sinc(t)

Question

Given the function:

$S(t) = sin(t/\Delta)/t$

How can one express this function in terms of:

$S(t) = sin(t)/t$

Thanks!

Answer 1

Suggestion: since they're different functions, give them different names. Say

$$ U(t) = \sin(t/\Delta) / t \\ S(t) = \sin(t)/t $$ Now, using substitution, try writing out and simplifying $$ U(\Delta s) $$ and comparing that to $$ S(s). $$