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Math Help - Help with trigonometric equation

  1. #1
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    Help with trigonometric equation

    Hi all, it's been a while since I took trigonometry in high school and I'm stuck on a current homework problem:

    Have to solve for what values of 't' make the equation = 0. 'w' is a constant not equal to 0.
    -w * sin(w * t) + sqrt(3) * w * cos(w * t) = 0

    I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:
    -w*(sin(w*t) - sqrt(3)*cos(w*t)) = 0

    I've tried setting sin(w*t) to cos(w*t + pi/2) and solving but I ran into problems.. If anyone could give me a hint to point me in the right direction that would be awesome, and maybe if you knew of a good trigonometry refresher kicking around on the internet that would be great as well.
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  2. #2
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    Quote Originally Posted by LnVII View Post
    Hi all, it's been a while since I took trigonometry in high school and I'm stuck on a current homework problem:

    Have to solve for what values of 't' make the equation = 0. 'w' is a constant not equal to 0.
    -w * sin(w * t) + sqrt(3) * w * cos(w * t) = 0

    I simplified it because I figured if 'w' is nonzero then only the inside terms mattered:
    -w*(sin(w*t) - sqrt(3)*cos(w*t)) = 0

    I've tried setting sin(w*t) to cos(w*t + pi/2) and solving but I ran into problems.. If anyone could give me a hint to point me in the right direction that would be awesome, and maybe if you knew of a good trigonometry refresher kicking around on the internet that would be great as well.
    <br />
-\omega \,sin(\omega t) + \omega \sqrt3 \,cos(\omega t) = 0

    \omega sin(\omega t) = \omega \sqrt3 \,cos(\omega t)

    \omega will cancel as it's non-zero. If t \neq 0

    We can divide through by cos(\omega t)

    \frac{sin(\omega t)}{cos (\omega t)} = \sqrt{3}

    Can you solve from there for t in terms of \omega?




    edit: The graph is attached for \omega = 2 and 0 \leq t \leq 2\pi
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  3. #3
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    So that would be
    <br />
tan(wt) = sqrt(3)<br />

    w*t = pi/3

    t = pi/3w

    So 't' would equal pi/3*w? Boy, was I overcomplicating that.. thanks so much for your help!
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  4. #4
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    Quote Originally Posted by LnVII View Post
    So that would be
    <br />
tan(wt) = sqrt(3)<br />

    w*t = pi/3

    t = pi/3w

    So 't' would equal pi/3*w? Boy, was I overcomplicating that.. thanks so much for your help!
    That is the main solution but there are others because tan(\omega t) will repeat itself every \frac{\pi}{\omega} radians on the t axis;

    <br />
t = \frac{\pi}{3\omega} + k \frac{\pi}{\omega} \: \: , \: k \in \mathbb{Z}
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