Question

What did sin theta/theta whisper worksheet answer key worksheet?

Answer 1

To evaluate
$\lim_{\theta \to 0} \frac{\sin\theta}{\theta}$

First, we input 0, for theta in the function to obtain:
$\frac{\sin0}{0} = \frac{0}{0}$

This is an indeterminate form.

So, we apply L'Hopital's rule by differentiating the numerator and the denominator as follows:

$\lim_{\theta \to 0} \frac{\sin\theta}{\theta}=\lim_{\theta \to 0} \frac{ \frac{d}{d\theta} (\sin\theta)}{\frac{d}{d\theta}\theta} \\ \\ =\lim_{\theta \to 0} \frac{\cos\theta}{1}=\cos0=1$