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

  1. #1
    ADH
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    Cool 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.
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    MHF Contributor
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    Quote Originally Posted by ADH View Post
    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.
    $\displaystyle \frac{\pi}{2} < x < \pi$

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

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

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

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

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

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

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

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