The limit of $\sin(x)$ as $x$ approaches 0 is given by:

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

This is because the sine function is continuous at $x = 0$, and $\sin(0)$ equals 0.

Would you like more details or have any questions?

Here are five related questions:

1. What is the limit of $\cos(x)$ as $x$ approaches 0?
2. How do you evaluate the limit $\lim_{{x \to 0}} \frac{\sin(x)}{x}$?
3. What is the derivative of $\sin(x)$ at $x = 0$?
4. How does the small-angle approximation $\sin(x) \approx x$ for $x$ near 0 relate to limits?
5. What is the Taylor series expansion of $\sin(x)$ around $x = 0$?

Tip: For very small angles (in radians), $\sin(x)$ is approximately equal to $x$, which is useful for simplifying expressions in calculus.