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Sinusoidal System (Posted on 2015-05-24) Difficulty: 3 of 5
Each solution to the system

y=sin(nx)
y=sin([n+1]x)
(where n is a positive integer) is also a solution to at least one of the following:

y=0
y=cos(ax)
y=-cos(ax)

Find, with proof, the value of a.

Also give a formula for the total number of solutions on the interval [0,2pi)

No Solution Yet Submitted by Jer    
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Thoughts | Comment 1 of 2
I arranged the first two equations into f(x) = sin([n+1]x) - sin(nx) = 0.  And then graphed it along with a few guesses for g(x) = cos(ax). Nothing seemed to look nice.  But then I switched to g(x) = sin(ax).  Then when a=2n+1 the zeros of f(x) coincided with some of the zeros of g(x).  So I'm not sure where cos(ax) comes in.
  Posted by Brian Smith on 2018-12-25 22:40:53
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