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Fantezi Cebir => Fantezi Cebir => Konuyu başlatan: stuart clark - Şubat 04, 2013, 04:37:24 ös

Başlık: Trigonometric Product
Gönderen: stuart clark - Şubat 04, 2013, 04:37:24 ös

How can I calculate (http://latex.codecogs.com/gif.latex?%5Chspace{-16}%5Cbf{%5Csin%20%5Cleft(%5Cfrac{%5Cpi}{7}%5Cright).%5Csin%20%5Cleft(%5Cfrac{2%5Cpi}{7}%5Cright).%5Csin%20%5Cleft(%5Cfrac{3%5Cpi}{7}%5Cright)=})

Başlık: Ynt: Trigonometric Product
Gönderen: alpercay - Şubat 04, 2013, 11:56:47 ös

sin(pi/2n+1).sin(2pi/2n+1).sin(3pi/2n+1)...sin(npi/2n+1) = sqrtr(2n+1)/2ⁿ

To see proof one can look up "Ussr Olympiad Problem Book,problem 231,page 334.But an elegant solution may be exist via using trigonometric identities, complex numbers or geometry.It is possible that calculate value of sin(pi/7) on triangle with 3pi/7,3pi/7 and pi/7 angles, but rather dull.Answer sqrt(7)/8.

Başlık: Ynt: Trigonometric Product
Gönderen: matsever44 - Şubat 09, 2013, 01:36:20 öö

fikir verebilir

Başlık: Ynt: Trigonometric Product
Gönderen: stuart clark - Şubat 09, 2013, 04:27:31 ös

Thanks Admin and Matsever44