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Thread: trig

  1. #1
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    trig

    when does sec2​x equal 4?
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    MHF Contributor MarkFL's Avatar
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    Re: trig

    Take the square root of both sides, then write in terms of cosine if that helps. What do you find?
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  3. #3
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    Re: trig

    pi/3... 2pi/3... 4pi/3... 5pi/3
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    MHF Contributor MarkFL's Avatar
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    Re: trig

    Yes, assuming we are given $\displaystyle 0\le x<2\pi$.
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    Re: trig

    or plus 2npi for each if not given that interval?
    Quote Originally Posted by MarkFL2 View Post
    Yes, assuming we are given $\displaystyle 0\le x<2\pi$.
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: trig

    We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\displaystyle \pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:

    $\displaystyle x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $\displaystyle k\in\mathbb{Z}$.
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    Re: trig

    Quote Originally Posted by MarkFL2 View Post
    We could shorten it since the 1st quadrant solution and the 3rd quadrant solutions differ by $\displaystyle \pi$, likewise for the 2nd and 4th quadrant roots, and so we could state:

    $\displaystyle x=\frac{\pi}{3}(3k+1),\,\frac{\pi}{3}(3k+2)$ where $\displaystyle k\in\mathbb{Z}$.
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