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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 with WolframAlpha cheating | Comment 4 of 5 |
Playing around with the equation the solution can be written as

x = sqrt(pi+1/4) - 1/2

Squaring x we see why: x^2 = pi - sqrt(pi+1/4) + 1/2 = pi - x.

Suddenly all the solutions make sense.  The families of solutions are all numbers that are appropriate shifts and/or reflections of x when squared.  

  Posted by Jer on 2018-11-16 12:24:13
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