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Thread: sin(x - pi/3) = 0

  1. #1
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    sin(x - pi/3) = 0

    "The Humongus Book of Trigonometry Problems" (by Kelley) has the problem

    sin (x - pi/3) = 0

    as one of their "Advanced Trigonometric Equations". After a bunch of steps, the answers for between 0 and 2*pi as:

    pi/3, 2pi/3, 4pi/3, 5pi/3

    How can 2pi/3 be a solution? I plug in and get sin(pi/3) and that is not zero. A similar problem with 5pi/2.
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  2. #2
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    Re: sin(x - pi/3) = 0

    Quote Originally Posted by duckey123 View Post
    "The Humongus Book of Trigonometry Problems" (by Kelley) has the problem
    sin (x - pi/3) = 0 as one of their "Advanced Trigonometric Equations". After a bunch of steps, the answers for between 0 and 2*pi as:
    pi/3, 2pi/3, 4pi/3, 5pi/3 How can 2pi/3 be a solution? I plug in and get sin(pi/3) and that is not zero. A similar problem with 5pi/2.

    $\displaystyle \sin \left( {\frac{\pi }{3} - \frac{\pi }{3}} \right) = 0\quad ,\;\sin \left( {\frac{{4\pi }}{3} - \frac{\pi }{3}} \right) = 0$
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  3. #3
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    Re: sin(x - pi/3) = 0

    Where did 2pi/3 and 5pi/3 come into play?
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  4. #4
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    Re: sin(x - pi/3) = 0

    Quote Originally Posted by duckey123 View Post
    Where did 2pi/3 and 5pi/3 come into play?
    Nowhere! There are only two solutions. See HERE.
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