Question

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

Answer 1

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

Solution.

So we must find coordinates of a point in the form $(x,0)$, that is we must find $x$:

$$f(x) = 2\cos x - 1 = 0$$

Solve this equation:

$$2\cos x = 1$$ $$\cos x = \frac{1}{2}$$ $$x = \pm \arccos \frac{1}{2} + 2\pi k, \quad k \in \mathbb{Z}$$ $$x = \pm \frac{\pi}{3} + 2\pi k, \quad k \in \mathbb{Z}$$

Answer:

$$\left(- \frac{\pi}{3} + 2\pi k, 0\right), \left(\frac{\pi}{3} + 2\pi k, 0\right), \quad k \in \mathbb{Z}$$