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Trigonometry $\frac{\pi} 7$
Posted: Wed Jul 13, 2011 1:38 am
by Labib
This is a plane Euclidean geometry I did not understand... The problem states::
sin$\frac\pi 7\cdot $ sin$\frac{2\pi} 7\cdot $ sin $\frac{3\pi} 7\cdot$ sin $\frac{4\pi} 7 \cdot $ sin$\frac{5\pi} 7 \cdot $sin $\frac{6\pi} 7 \cdot $ sin $\frac{7\pi} 7 $ = $\frac 7 {64}$
(Source ::
)
Need help urgently!!
sin$\frac{7\pi} 7 = 0$, so how come this be proved!!
Re: Trigonometry $\frac{\pi} 7$
Posted: Wed Jul 13, 2011 12:49 pm
by confused
uestion ta ki tik ase
Re: Trigonometry $\frac{\pi} 7$
Posted: Wed Jul 13, 2011 11:54 pm
by Labib
100% @ confused.... I didn't make any mistake stating the problem....
There was a hint as well. I tried using it but didn't get much out of it!!!
I'll post the hint here.
Hint::
Re: Trigonometry $\frac{\pi} 7$
Posted: Thu Jul 14, 2011 12:29 am
by Labib
I believe I've posted this problem in the wrong Forum....
It should be moved to the Geometry forum....
If any of the admins could please help me out....
Re: Trigonometry $\frac{\pi} 7$
Posted: Fri Jul 15, 2011 12:11 am
by Labib
I've also created an AOPS topic for this problem....
Here's the link:::
http://www.artofproblemsolving.com/Foru ... 3#p2358903
Re: Trigonometry $\frac{\pi} 7$
Posted: Tue Jul 19, 2011 11:07 am
by nisha
maybe its wrong!
Re: Trigonometry $\frac{\pi} 7$
Posted: Tue Jul 19, 2011 3:36 pm
by leonardo shawon
u can use this formula
http://www.artofproblemsolving.com/Foru ... hilit=trig
I also think as Nisha said that the given expression isnot valid. whats ur opinion?
Re: Trigonometry $\frac{\pi} 7$
Posted: Wed Jul 20, 2011 11:51 pm
by Labib
This was the theorem I saw::
$n~(\geq 2)$ is a natural number.
$\prod_{k=1}^{n-1}\sin\frac{k\pi}{n}=\frac{n}{2^{n-1}}$
I still believe the problem's invalid!
Re: Trigonometry $\frac{\pi} 7$
Posted: Thu Jul 21, 2011 12:03 am
by leonardo shawon
it will be invalid if the sin 7pi/7=0