MHB Sin Values of 87 and 89 Degrees

[juantheron]

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]

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, \(4.0194366942304562\times 10^{-14}\)

 

[juantheron]

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]

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 http://www.mathhelpboards.com/showthread.php?253-Simplify-cos(a)cos(2a)cos(3a)-cos(999a)-if-a-(2pi)-1999&p=1517&viewfull=1#post1517, noting that $x=\pm1^\circ,\pm3^\circ,\pm5^\circ,\ldots,\pm89 ^\circ$ are the solutions of the equation $\cos(90x) = 0.$