A Cosine Graph and the Smallest Integer Solution

★ 6/10functions trigonometry Trigonometric Identities Symmetry

Problem

The figure shows part of the graph of the function $f(x)=2\cos(\omega x+\varphi)$ , where $\omega>0$ ; the graph attains the value $2$ at $x=\dfrac{13\pi}{12}$ and crosses the $x$ -axis at $x=\dfrac{\pi}{3}$ , as marked.

Find the smallest positive integer $x$ satisfying

\left(f(x)-f\left(-\frac{7\pi}{4}\right)\right)\left(f(x)-f\left(\frac{4\pi}{3}\right)\right)>0.

Answer

Solution

Difficulty	6/10
Topics	functions, trigonometry, Trigonometric Identities, Symmetry

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