1. Summation

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!

2. Originally Posted by Tangera
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!
Well first make things easy for yourself by adjusting the summation limits:

$\displaystyle \sum_{r=11}^{28} \sin(\pi/(r-10)) =\sum_{r=1}^{18} \sin(\pi/r)$

RonL

3. Hello! Erm....could you give me more hints as to how to solve the problem. I am still stuck. >.< Thank you!

4. Originally Posted by CaptainBlack
Well first make things easy for yourself by adjusting the summation limits:

$\displaystyle \sum_{r=11}^{28} \sin(\pi/(r-10)) =\sum_{r=1}^{18} \sin(\pi/r)$

RonL
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

$\displaystyle \sin\bigg(\frac{\pi}{18}\bigg)=\frac{1}{2}\sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2+...}}}}$

$\displaystyle \sum_{r=1}^{18}\sin\bigg(\frac{\pi}{n}\bigg)=6.891$