Approximating θ/2 as θ for small angles: Is the error significant?

[physics user1]

θ/2 as θ if θ is a small angle?

Thanks

 

[S.G. Janssens]

That depends on how you quantify the error. For example, both angles are $O(\theta)$ of course, but the relative error is still $O(1)$. By the latter I mean that
$$
\frac{\left|\frac{\theta}{2} - \theta \right|}{\left|\frac{\theta}{2}\right|} = 1
$$