Re: sines problem

In article <1172771839.577321.75720@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
olegtsodikov@xxxxxxxxx wrote:

On Mar 1, 12:41 pm, jankri...@xxxxxxxxxxx wrote:
On 1 Mar, 18:32, olegtsodi...@xxxxxxxxx wrote:
On 1 Mar, 18:11, olegtsodi...@xxxxxxxxx wrote:

If we have a finite set of angles, phi_i (i=1,2,...,N<inf), then can
one always find an integer n>0 such that
sin(n*phi_i) are all non-negative ?
....
If this is homework, I think that hint is enough. OK, one more: phi_1
could be 1....

I haven't had homework for many years. If you choose not to post the
counterexample, that's fine. Remove your post then.
Thanks.


Please don't take offence. On the internet it's easy to
misunderstand people's attitudes because you can't see their faces, and
Jan Haugland really was trying to be helpful.

Quite often, lazy students do post their homework problems to
mathematical news groups. We try to guess when that has happened, and
respond in a guarded way. This time Jan guessed wrongly: that's all.

For a counter-example, choose N = 2, phi_1 = - phi_2 = something
which is not a rational multiple of pi, for example 1 radian (as Jan
suggested). Can you see why that works?

Ken Pledger.
.

Quantcast