Mathematics

The sine function's Taylor series $\sin x = x - \frac{x^3}{3!} + \cdots$ is derived assuming $x$ is in radians, so $\frac{\sin x}{x} \to 1$ as $x \to 0$. If $x$ were in degrees, you'd need a conversion factor: $\sin(x°) = \sin\left(\frac{\pi x}{180}\right)$, which introduces $\frac{\pi}{180}$ into the limit and changes the answer to $\frac{\pi}{180}$ instead of $1$.

The sine function's Taylor series $\sin x = x - \frac{x^3}{3!} + \cdots$ is derived assuming $x$ is in radians, so $\frac{\sin x}{x} \to 1$ as $x \to 0$. If $x$ were in degrees, you'd need a conversion factor: $\sin(x°) = \sin\left(\frac{\pi x}{180}\right)$, which introduces $\frac{\pi}{180}$ into the limit and changes the answer to $\frac{\pi}{180}$ instead of $1$.