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Thread: All solutions for trig equation

  1. #1
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    All solutions for trig equation

    Find all solutions for each of the following in ther given intervals:

    $\displaystyle (a) tan^2(x) = 3,~ -2\pi<x\le\pi$

    $\displaystyle (b) sin^2(x) = \frac{1}{2},~ \frac{\pi}{2}\le x\le2\pi$

    (a)

    $\displaystyle tan(x) = \sqrt3 $

    Do I find only the values that are positive $\displaystyle \sqrt{3}$ in the given interval? i.e., $\displaystyle \frac{\pi}{3}$, $\displaystyle -\frac{2\pi}{3}$, $\displaystyle -\frac{5\pi}{3} $ or do I just find every value where $\displaystyle tan(x) = \sqrt3 $?, i.e, 60, 180-60, -60, -180-(-60), -180+(-60), -360-(-60)

    (b)

    same deal accept with $\displaystyle \frac{\pi}{4}$
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  2. #2
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    Re: All solutions for trig equation

    Quote Originally Posted by terrorsquid View Post
    Find all solutions for each of the following in ther given intervals:

    $\displaystyle (a) tan^2(x) = 3,~ -2\pi<x\le\pi$

    $\displaystyle (b) sin^2(x) = \frac{1}{2},~ \frac{\pi}{2}\le x\le2\pi$

    (a)

    $\displaystyle tan(x) = \sqrt3 $

    Do I find only the values that are positive $\displaystyle \sqrt{3}$ in the given interval? i.e., $\displaystyle \frac{\pi}{3}$, $\displaystyle -\frac{2\pi}{3}$, $\displaystyle -\frac{5\pi}{3} $ or do I just find every value where $\displaystyle tan(x) = \sqrt3 $?, i.e, 60, 180-60, -60, -180-(-60), -180+(-60), -360-(-60)

    (b)

    same deal accept with $\displaystyle \frac{\pi}{4}$
    Well first of all $\displaystyle \displaystyle \tan^2{x} = 3 \implies \tan{x} = \pm \sqrt{3} $, not $\displaystyle \displaystyle \sqrt{3}$...
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  3. #3
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    Re: All solutions for trig equation

    ah ok, thanks. So it is everything.
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