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)
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.
Thoughts
