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Sine of Squared (Posted on 2018-11-15) Difficulty: 3 of 5
The smallest positive solution to sin x = sin x2 is x = 1.

What is the second smallest positive solution?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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Solution computer solution | Comment 2 of 5 |
The partial output of the program shown below shows that the sign of the difference between the two sides changes between x=1.341627718511  and x=1.341627718512. Judging by the sizes of the differences from zero one would assume the answer is closer to the former number than the latter.

...
1.341627718504   -6.25699492218246E-12
1.341627718505   -5.42021982852248E-12
1.341627718506   -4.5834447348625E-12
1.341627718507   -3.74666964120252E-12
1.341627718508   -2.90978352524007E-12
1.341627718509   -2.07300843158009E-12
1.34162771851   -1.23634436022257E-12
1.341627718511   -3.99347221957669E-13
1.341627718512    4.37316849399849E-13
1.341627718513    1.27409194305983E-12
1.341627718514    2.11097805902227E-12
1.341627718515    2.94775315268225E-12
1.341627718516    3.78452824634223E-12
1.341627718517    4.62130334000221E-12
1.341627718518    5.45807843366219E-12
...

The code portion shown is the result of successive restrictions on the range and precision of the x values:

 For x = 1.3416277185 To 1.3416277186 Step 0.000000000001
   y = Sin(x) - Sin(x * x)
   Text1.Text = Text1.Text & x & "   " & Str(y) & crlf
   DoEvents
 Next


  Posted by Charlie on 2018-11-15 11:17:41
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