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=== Motion of a pendulum ===
{{main|Pendulum (mechanics)#Small-angle approximation}}
The second-order cosine approximation is especially useful in calculating the [[potential energy]] of a [[pendulum]], which can then be applied with a [[Lagrangian mechanics|Lagrangian]] to find the indirect (energy) equation of motion. When calculating the [[frequency|period]] of a simple pendulum, the small-angle approximation for sine is used to allow the resulting differential equation to be solved easily by comparison with the differential equation describing [[simple harmonic motion]].<ref>{{cite journal |last=Bissell |first=John J. |year=2025 |title=Proof of the small angle approximation {{tmath|\sin \theta \approx \theta}} using the geometry and motion of a simple pendulum |journal=International Journal of Mathematical Education in Science and Technology |volume=56 |number=3 |pages=548–554 |doi=10.1080/0020739X.2023.2258885 }}</ref>
===Optics===
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