Why is

[math]

\lim_{t\to0} \frac{\sin(t)

}{t} = 1

[/math]

You could use L'Hopital's Rule on it.

 

[math]\lim_{t\to 0} \frac{\sin t}{t} = \lim_{t \to 0} \frac{\cos t}{1} = 1[/math]

You can also prove this limit using the squeeze theorem. Here is

which shows the proof fairly nicely.

Of course. Thank you both for reminding me.