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 Trigonometric product (Posted on 2013-12-29)
Compute the infinite product

[sin(x) cos(x/2)]^1/2 · [sin(x/2) cos(x/4)]^1/4 · [sin(x/4) cos(x/8)]^1/8 · ... ,

where 0 ≤ x ≤ 2π

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 computer exploration--table of values | Comment 1 of 4
`list   10   for Xn=1 to 20:X=Xn/10   20   Deno=1:Deno2=2:A=1   30   for F=1 to 60   40    Fctr=(sin(X/Deno)*cos(X/(Deno2)))^(1/(Deno2))   50    A=A*Fctr   70    Deno=Deno2:Deno2=Deno2*2   80   next   90   print X,using(1,8),A,asin(A)  100   nextrun`
`  x      expression      arcsin(expression) 0.1     0.04991671      0.04993746 0.2     0.09933467      0.09949876 0.3     0.14776010      0.14830313 0.4     0.19470917      0.19596094 0.5     0.23971277      0.24206998 0.6     0.28232124      0.28621292 0.7     0.32210884      0.32795621 0.8     0.35867805      0.36685132 0.9     0.39166345      0.40243879 1.0     0.42073549      0.43425591 1.1     0.44560368      0.46184848 1.2     0.46601954      0.48478658 1.3     0.48177909      0.50268383 1.4     0.49272486      0.51521835 1.5     0.49874749      0.52215311 1.6     0.49978680      0.52335261 1.7     0.49583241      0.51879310 1.8     0.48692382      0.50856438 1.9     0.47315004      0.49286296 2.0     0.45464871      0.47197777OK`

Edited on December 29, 2013, 1:28 pm
 Posted by Charlie on 2013-12-29 13:26:28

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