1. **Problem:** Find the limit $$\lim_{\theta \to 0} \frac{\sin \theta}{\theta}$$. 2. **Formula and Rule:** The fundamental limit is $$\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$$. This is a standard trigonometric limit used frequently in calculus. 3. **Explanation:** As $$\theta$$ approaches 0, the ratio of $$\sin \theta$$ to $$\theta$$ approaches 1 because the sine function behaves like its angle in radians near zero. 4. **Intermediate Work:** No further simplification is needed as this is a well-known limit. 5. **Final Answer:** $$\boxed{1}$$. --- **Slug:** sin-theta-over-theta **Subject:** calculus **Desmos:** {"latex":"y=\frac{\sin x}{x}","features":{"intercepts":true,"extrema":true}} **q_count:** 1