Hello! Thank you for helping me with this question! I have no idea how do I sum trigonometric function! [Or are we supposed to use summation by method of difference?]
Evaluate the following:
28
∑ sin [pi / (r-10)]
r=11
Thank you very much!
I dont see an easy way of doing this
It looks as though you will just have to muddle through it the hard way and do this
$\displaystyle \sum_{r=1}^{18}\sin\bigg(\frac{\pi}{r}\bigg)=\sin( \pi)+\sin\bigg(\frac{\pi}{2}\bigg)+...+\sin\bigg(\ frac{\pi}{18}\bigg)$
Which is equal to $\displaystyle 0+1+...+0.174$ ....You can't really do exact values because for example
$\displaystyle \sin\bigg(\frac{\pi}{18}\bigg)$
Is given by the infinitely nested radical
$\displaystyle \sin\bigg(\frac{\pi}{18}\bigg)=\frac{1}{2}\sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2+...}}}}$
But if it is helpful mathcad says
$\displaystyle \sum_{r=1}^{18}\sin\bigg(\frac{\pi}{n}\bigg)=6.891$