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Math Help - Solving Tri equation

  1. #1
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    Solving Tri equation

    Having trouble with this question.

    Determine exact solutions for sin3x + square root 3 / 2 =0, where 0 <= theta <= 2 pi
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  2. #2
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by Neconine View Post
    Having trouble with this question.

    Determine exact solutions for sin3x + square root 3 / 2 =0, where 0 <= theta <= 2 pi

     \sin 3x + \frac{\sqrt{3}}{2} = 0

    \sin 3x = \frac{-\sqrt{3}}{2}

    3x = \pi + \frac{\pi}{3} \Rightarrow x = \frac{4\pi}{9}

    3x = 2\pi - \frac{\pi}{3} \Rightarrow x = \frac{5\pi}{9}

    in general

     \sin 3x = \frac{-\sqrt{3}}{2}

     3x = \pi + \frac{\pi}{3} + 2n\pi n natural number 0,1,2,3,... take the numbers such that 0\leq x \leq 2 \pi

    or

    3x = 2\pi - \frac{\pi}{3} + 2n\pi n is like above
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  3. #3
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    São Tomé
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    help for the exercise

    Hello Neconine,
    I agree with Amer.
    The attachment shows one of the possible ways to solve the equation.
    I hope you understand!
    Bye!
    Attached Thumbnails Attached Thumbnails Solving Tri equation-equation-trig.jpg  
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  4. #4
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    Thanks to the both of you.

    You have been a great help, I really appreciate this.
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