 Small-angle approximation

As $x\to 0$, the limit $\sin x/x\to 1$ gives $\sin x\sim x$, while the Taylor series gives $\arcsin x\sim x$ and $\cos x\sim 1-x^2/2$.

The small-angle approximation is a mathematical simplification used in various fields of physics and engineering when dealing with angles that are small (typically measured in radians). The key idea behind this approximation is that for small angles, certain trigonometric functions can be approximated by their corresponding linear values. Specifically, if \(\theta\) is a small angle (in radians), the following approximations hold: 1. \(\sin(\theta) \approx \theta\) 2.