True/False: sin 3x/3x = sin 1

**Mathless** · February 10th 2010, 12:09 AM

Fairly sure the answer is false as you can't just cancel out the 3x's, but it asks to correct it too [that's where I'm stumped]. Can sin (3x) / 3x be factored down anymore than that? I really have no idea what the teacher is asking.

**CaptainBlack** · February 10th 2010, 12:15 AM

Originally Posted by Mathless

Fairly sure the answer is false as you can't just cancel out the 3x's, but it asks to correct it too [that's where I'm stumped]. Can sin (3x) / 3x be factored down anymore than that? I really have no idea what the teacher is asking.

It is false, if you have done limits you can write:

$\lim_{x \to 0} \frac{\sin(3x)}{3x}=1$

or for small $x$ :

$\frac{\sin(3x)}{3x}\approx 1$

CB

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