Tag: arithmetic-progressions

trigonometry – How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?

The Question : 156 people think this question is useful How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series: $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$ There