Question

In a pendulum, why is the small angle approximation used, even though large angles are involved?

Answer 1

The approximation \(\cos \theta \approx 1- \Large \frac {\theta ^2}{2}\)
leading to a linear differential equation is valid to 1% up to \(\theta = 0.7\, rad = 40°\)

Usually, 'small' amplitude is kept within 20°, so there is no problem.

Answer 2

Are there similar bounds for\[\sin \theta= \theta\]?

Answer 3

Oh, you can derive one from the other. Thank you