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Given the function:

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

How can one express this function in terms of:

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

Thanks!

user2398029
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  • Welcome to MSE! What have you tried so far? Telling us well help us better answer your question. – John Hughes Sep 16 '15 at 17:12
  • So far, I've tried expanding each side into their complex exponential forms, then isolating t on both sides and trying to solve the equation. That's not been getting me anywhere. – user2398029 Sep 16 '15 at 17:27

1 Answers1

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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 $$ S(s). $$

John Hughes
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  • Thanks for your help. This gives me $U(\Deltas)=\DeltaS(s)$, but I can't seem to find a value of $s$ that results in relating $sin(t/\Delta)$ to $sin(t)$. Maybe I'm missing something obvious, or not aiming for the right thing here. – user2398029 Sep 16 '15 at 22:12
  • Essentially everything I'm writing down simplifies to $sin(t) = sin(t)$ or $sin(t/\Delta)=sin(t/\Delta)$. – user2398029 Sep 16 '15 at 22:16
  • You got $U(\Delta s) = \Delta S(s)$. If you substitute $t = \Delta s$, i.e., $s = t/\Delta$, you get $U(t) = \Delta S(t/\Delta)$. And that's about all you can hope for. It expresses $U(t)$ in terms of the function $S$...just not $S(t)$. There's no simple formula, in general, for relating $\sin(ct)$ to $\sin(t)$ when $c$ is not an integer. – John Hughes Sep 17 '15 at 01:12
  • Right, so I guess I wasn't looking for a more explicit relation than what is possible. Thanks for pointing me in the right direction. – user2398029 Sep 17 '15 at 01:17