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)
(In reply to
Thoughts by Brian Smith)
I posted this problem so long ago I'm not sure what I intended.
The zeros of f(x) only give the x-coordinates of the solutions to the system. You want a cosine that crosses the intersection points of sine.
This desmos graph is a hint
https://www.desmos.com/calculator/72kefffiw0
In playing with that graph I realize I should have asked for the least value of a for any given n.
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Posted by Jer
on 2018-12-26 11:58:55 |
re: Thoughts
