Question

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

A. x=π/6
B. x=π/4
C. x=π/3
D. x=π/8

Answer 1

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

A. $x = \pi /6$

B. $x = \pi /4$

C. $x = \pi / 3$

D. $x = \pi / 8$

Solution:

Graph of the X-axis - Y-coordinate equals to zero:

$$f (x) = 2 \cos x - 1$$ $$g (x) = 0$$ $$f (x) = g (x)$$ $$2 \cos x - 1 = 0$$$$\cos x = \frac {1}{2}$$ $$x = \pm \frac {\pi}{3} + 2 \pi n, n \in Z$$

We are looking for solution in the range from 0 to $\pi$ :

$$n = 0 \rightarrow x = \frac {\pi}{3} + 2 \pi n = \frac {\pi}{3}$$

Answer: $C.x = \frac{\pi}{3}$