Question

At what point the graph of f(x) = 2cos x – 1 intersects the x-axis?

Answer 1

Suppose the graph of $f(x)$ intersects the x-axis at point $M(x_0, 0)$. Hence:

$f(x_0) = 0;$

$2\cos x_0 - 1 = 0;$

$2\cos x_0 = 1;$

$\cos x_0 = 0.5;$

$x_0 = \pm \arccos 0.5 + 2\pi n, n \in Z;$

$x_0 = \pm \frac{\pi}{3} + 2\pi n, n \in Z.$

Thus $f(x)$ intersects the x-axis at points $M(\pm \frac{\pi}{3} + 2\pi n, 0), n \in Z$.

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