# Find all the zeros of this function: f(x) = 1 - 3cos(2x) in this interval?

• Sep 22nd 2010, 04:46 PM
Find all the zeros of this function: f(x) = 1 - 3cos(2x) in this interval?
Find all the zeros of this function: f(x) = 1 - 3cos(2x) in the interval (pi/2 is less than/equal to x less then equal to pi.

Thank you.
• Sep 22nd 2010, 06:24 PM
skeeter
Quote:

Find all the zeros of this function: f(x) = 1 - 3cos(2x) in the interval (pi/2 is less than/equal to x less then equal to pi.

Thank you.

$\frac{\pi}{2} < x < \pi$

$\pi < 2x < 2\pi$

let $u = 2x$ ...

$1 - 3\cos(u) = 0$

$\cos(u) = \frac{1}{3}$

$u$ is in quad IV , so ...

$u = 2\pi - \arccos\left(\frac{1}{3}\right)$

$2x = 2\pi - \arccos\left(\frac{1}{3}\right)$

$x = \pi - \frac{1}{2}\arccos\left(\frac{1}{3}\right)$