Roots of Trigonometric Functions in an Interval

[Ted123]

Homework Statement

This isn't really a question on its own, rather a step in the solution to another question:

How would I prove that [tex]y= A\cos x + B\sin x[/tex] (A, B arbitrary constants) has at least [tex]n[/tex] zeroes in the interval [tex][\pi , \pi (n+1)][/tex] where [tex]n\in\mathbb{Z}\;?[/tex]

(I don't need to be too explicit about it)

I was thinking state that [tex]A\cos x + B\sin x = \sqrt{A^2+B^2}\cos (x + \alpha)[/tex] [tex]0\leq\alpha \leq 2\pi[/tex] and say something about periodicity and when sine and cosine are + or -...

 

[grey_earl]

Should be it. Don't forget to mention that α = -arccos(A/sqrt(A²+B²)).