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Math Help - How many values of x

  1. #1
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    Post How many values of x

    For how many values of in the interval
    is ?
    A.

    B.

    C.

    D.

    E.
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  2. #2
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    \displaystyle \cos{(4x)} = 0

    \displaystyle 4x = \arccos{(0)}

    \displaystyle 4x = \frac{\pi}{2} + \pi n where \displaystyle n \in \mathbf{Z}

    \displaystyle x = \frac{\pi}{8} + \frac{\pi n}{4}

    \displaystyle x = \frac{\pi + 2\pi n}{8}.


    How many values will lie in the region \displaystyle \pi \leq x \leq 3\pi?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    \displaystyle \cos{(4x)} = 0

    \displaystyle 4x = \arccos{(0)}

    \displaystyle 4x = \frac{\pi}{2} + \pi n where \displaystyle n \in \mathbf{Z}

    \displaystyle x = \frac{\pi}{8} + \frac{\pi n}{4}

    \displaystyle x = \frac{\pi + 2\pi n}{8}.


    How many values will lie in the region \displaystyle \pi \leq x \leq 3\pi?
    Technically, the second line should read

    \displaystyle 4x = \arccos{(0)}+ \pi n where \displaystyle n \in \mathbf{Z}

    since \displaystyle \arccos{x} is a function.
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  4. #4
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    Actually some textbooks use "arccos" (and "arcsin") to include all solutions (so they are NOT functions) and "Arccos" (and "Arcsin") for the functions.
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