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Trigonometric product (Posted on 2013-12-29) Difficulty: 2 of 5
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    
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Some Thoughts 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   next
run
  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      0.47197777
OK

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

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