What is $\lim\limits_{\theta \rightarrow0} \frac{sin \theta}{\theta}$ equal to?

This is one of the most important standard limits in calculus: as θ approaches 0 (measured in radians), sin θ and θ become arbitrarily close in value, so their ratio approaches exactly 1. It can be proven geometrically by comparing the areas of a triangle, a circular sector, and another triangle bounding sin θ, θ, and tan θ, then applying the squeeze theorem. This limit underlies the derivative of sin(x) being cos(x).

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