Small Angle Approximations (Edexcel A-Level Mathematics): Flashcards

$\sin \theta \approx \theta$

$\cos \theta \approx 1 - \theta^2/2$

$\tan \theta \approx \theta$

$\sin \theta$ approaches $\theta$ as $\theta$ approaches $0$.

Taylor series expansions around $\theta = 0$.

In physics, engineering, and calculus.

$\sin(0.1) \approx 0.1$

$\cos(0.05) \approx 0.99875$

$\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$

They simplify calculations involving small angles.