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

Thread starter physics user1
Start date Jan 13, 2016
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In summary, for small angles, it is often acceptable to approximate θ/2 as θ without significant error. This is because for small values of θ, the difference between θ/2 and θ is negligible and does not significantly impact the overall calculation or measurement. However, for larger angles, the error can become more significant and may need to be taken into account. It is important to consider the size of the angle and the required level of accuracy when determining whether θ/2 can be approximated as θ.

Jan 13, 2016

physics user1

θ/2 as θ if θ is a small angle?

Thanks

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Jan 13, 2016

S.G. Janssens

Science Advisor

Education Advisor

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
$$
\frac{\left|\frac{\theta}{2} - \theta \right|}{\left|\frac{\theta}{2}\right|} = 1
$$

Last edited: Jan 13, 2016

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