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Trigonometry Trig. product

jacks

Well-known member
Apr 5, 2012
226
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree
Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, \(4.0194366942304562\times 10^{-14}\)
 

jacks

Well-known member
Apr 5, 2012
226
Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, \(4.0194366942304562\times 10^{-14}\)
Thanks Sudhakara

I am trying to find it with the help of complex no.(like nth -roots of unity)
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,708
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree
Follow the method used in this thread, noting that $x=\pm1^\circ,\pm3^\circ,\pm5^\circ,\ldots,\pm89 ^\circ$ are the solutions of the equation $\cos(90x) = 0.$