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

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

I was thinking state that $$A\cos x + B\sin x = \sqrt{A^2+B^2}\cos (x + \alpha)$$ $$0\leq\alpha \leq 2\pi$$ 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)).