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Math Help - Find solutions for this equation in the intervals given:

  1. #1
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    Find solutions for this equation in the intervals given:

    Find all solutions for each of the following equations in the intervals given:
    a)  sin^2x = \frac{1}{4}, \frac{\pi}{2}<=x<2\pi;

    b)  tan^2x = 1, {-\pi}<=x<\pi;

    how would i attack these questions? if you could explain i would really appreciate it. thank u
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    Find all solutions for each of the following equations in the intervals given:
    a)  sin^2x = \frac{1}{4}, \frac{\pi}{2}<=x<2\pi;

    b)  tan^2x = 1, {-\pi}<=x<\pi;

    how would i attack these questions? if you could explain i would really appreciate it. thank u
    a) \sin^2{x} - \frac{1}{4} = 0

    \left(\sin{x} + \frac{1}{2}\right)\left(\sin{x} - \frac{1}{2}\right) = 0

    \sin{x} = -\frac{1}{2} ... x = \frac{7\pi}{6} ... x = \frac{11\pi}{6}

    \sin{x} = \frac{1}{2} ... x = \frac{5\pi}{6}

    b) \tan^2{x} - 1 = 0

    finish up by factoring ... you should get x = \pm \frac{\pi}{4} and x = \pm \frac{3\pi}{4}
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