Finding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$ I need help understanding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$ or $\displaystyle \sum_{i=0}^{180} \sin(i)$ 
This might be related to a formula to find the average voltage from a generator used to gauge waves: $V_\text{avg} = 0.637 \times V_\text{peak}$. I am currently learning about AC circuits in the military. 

Wikipedia says
$$\sum_{k=0}^n \sin{(\gamma + k\alpha)} = \frac{\sin\tfrac{(n+1)\alpha}{2} + \sin{(\gamma + \tfrac{n\alpha}{2})}}{\sin\tfrac\alpha2}$$So we may write $\gamma = 0$, $n=180$ and $\alpha=\frac{\pi}{180}$ to get $$\sum_{k=0}^{180} \sin{\tfrac{k\pi}{180}} = \frac{\sin\tfrac{181\pi}{360} \sin\tfrac{\pi}{2}}{\sin\tfrac{\pi}{720}} = \frac{\sin\tfrac{181\pi}{360} }{\sin\tfrac{\pi}{720}}$$
A proof of the formula can be found here.
