Aperiodic Monotonic Trigonometric Divergent Series

INFRASPECIES

$\displaystyle \sum_{n\geq a} \sin n = \dfrac{1}{2} \left(\sin a + \cos a \cot\frac{1}{2} \right) = \dfrac{1}{2} \, \csc\dfrac{1}{2} \, \cos\left(\dfrac{1}{2} - a\right)$ (stable)

$\displaystyle \sum_{n\geq a} \cos n = \dfrac{1}{2} \left(\cos a - \sin a \cot\frac{1}{2} \right) = \dfrac{1}{2} \, \csc\dfrac{1}{2} \, \sin\left(\dfrac{1}{2} - a\right)$ (stable)

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