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, 03:46 PMADHFind 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, 05:24 PMskeeter
$\displaystyle \frac{\pi}{2} < x < \pi$

$\displaystyle \pi < 2x < 2\pi$

let $\displaystyle u = 2x$ ...

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

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

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

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

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

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