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Thread: Solving For 'X' Using Trigonometry

  1. #1
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    Solving For 'X' Using Trigonometry

    Hi there!
    I am just wondering how you would solve for this?
    Solve the equation sin(3x/2) = 1/2 for x E (-pi, pi)

    Any help much appreciated,
    Thanks in advance!
    ~Ebony Jade :-)
    Last edited by EbonyJade; May 6th 2017 at 07:50 PM.
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  2. #2
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    Re: Solving For 'X' Using Trigonometry

    For what values of $\theta$ do you have $\sin \theta = \dfrac{1}{2}$? You should know the table:

    $\begin{matrix}\theta & \sin \theta \\ 0 & 0 \\ \dfrac{\pi}{6} & \dfrac{1}{2} \\ \dfrac{\pi}{4} & \dfrac{\sqrt{2}}{2} \\ \dfrac{\pi}{3} & \dfrac{\sqrt{3}}{2} \\ \dfrac{\pi}{2} & 1\end{matrix}$

    Now, in the interval $x \in (-\pi,\pi)$, will you have any other possible values for $\theta$? How can you tell? Once you have all possible values for $\theta$, you have $\theta = \dfrac{3x}{2}$. Solve for $x$. (Hint: you should find three possible values for $\theta$ where $x \in (-\pi,\pi)$).
    Last edited by SlipEternal; May 6th 2017 at 07:42 PM.
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  3. #3
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    Re: Solving For 'X' Using Trigonometry

    Quote Originally Posted by EbonyJade View Post
    Hi there!
    I am just wondering how you would solve for this?
    Solve the equation sin(3x/2) = 1/2 for x E (-pie, pie)Any help much appreciated,
    One eats pie. One calculates with the number pi That is $\pi$.

    If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$
    Thanks from EbonyJade
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  4. #4
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    Re: Solving For 'X' Using Trigonometry

    Quote Originally Posted by Plato View Post
    One eats pie. One calculates with the number pi That is $\pi$.

    If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$
    Or, $\theta = \dfrac{5\pi}{6}-2\pi = -\dfrac{7\pi}{6}$
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  5. #5
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    Re: Solving For 'X' Using Trigonometry

    Quote Originally Posted by SlipEternal View Post
    For what values of $\theta$ do you have $\sin \theta = \dfrac{1}{2}$? You should know the table:

    $\begin{matrix}\theta & \sin \theta \\ 0 & 0 \\ \dfrac{\pi}{6} & \dfrac{1}{2} \\ \dfrac{\pi}{4} & \dfrac{\sqrt{2}}{2} \\ \dfrac{\pi}{3} & \dfrac{\sqrt{3}}{2} \\ \dfrac{\pi}{2} & 1\end{matrix}$

    Now, in the interval $x \in (-\pi,\pi)$, will you have any other possible values for $\theta$? How can you tell? Once you have all possible values for $\theta$, you have $\theta = \dfrac{3x}{2}$. Solve for $x$. (Hint: you should find three possible values for $\theta$ where $x \in (-\pi,\pi)$).
    Awesome thanks SlipEternal!
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  6. #6
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    Re: Solving For 'X' Using Trigonometry

    Quote Originally Posted by Plato View Post
    One eats pie. One calculates with the number pi That is $\pi$.

    If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$

    Haha! Thanks Plato! Just realised!
    Whoops!!
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  7. #7
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    Re: Solving For 'X' Using Trigonometry

    ....................
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