What is the period of $\sin 2\theta + \sin \frac{\theta}{2}$? The period of the first term is $\pi$ and that of the second is $4\pi$. Does that mean that the period of the whole is $4\pi$?
2026-04-01 06:55:48.1775026548
What is the period of $\sin 2\theta + \sin \frac{\theta}{2}$
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It is equal to the smallest $>0$ generator of $2\mathbf{Z} \cap \frac{1}{2}\mathbf{Z}$ as $\mathbf{Z}$-module. So what is the smallest $a\in\mathbf{Q}_{+}^{\times}$ such that $2\mathbf{Z} \cap \frac{1}{2}\mathbf{Z} = a \mathbf{Z}$ ?