To evaluate [tex]\lim_{\theta \rightarrow 0} ( \frac{sin \theta}{\theta} )[/tex]
Note that
[tex]sin(x) = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \, ..., [/tex]
Therefore, for small values of x,
[tex]sin(x) \approx 1 - \frac{x^{2}}{3!} + \, ..., \approx 1 [/tex]
Answer:
[tex]lim_{\theta \rightarrow 0} \frac{sin \theta}{\theta} = 1 [/tex]
