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Math Help - The double angle

  1. #1
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    The double angle

    Hey guys, was just revising some trig work and came across a problem.

    If you were told that sinx is pie/2 < x < pie, is sin3x still the same domain, or would it become 3pie/2 < 3x < 3pie. If this is the case then does that mean sin3x can have 2 values, one positive one negative?
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  2. #2
    Junior Member ibnashraf's Avatar
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    Given that the domain for sin x is \frac {\pi}{2}<x<\pi \Rightarrow the domain for sin 3x will be \frac {3\pi}{2}<3x<3\pi

    Lets say that when you solve for sin x, you get x = \alpha, \beta for the domain \frac {\pi}{2}<x<\pi

    Now to find for 3x, this means 3 revolutions, that is,

    1st revolution, x = \alpha, \beta
    2nd revolution, 2x = \alpha, \beta, \alpha+2\pi, \beta+2\pi , (where 2\pi radians is one revolution or 360 degrees.)
    3rd revolution, 3x = \alpha, \beta, \alpha+2\pi, \beta+2\pi, \alpha+2\pi+2\pi, \beta+2\pi+2\pi

    So this 3rd revolution, that is for 3x, would be for the domain \frac {3\pi}{2}<3x<3\pi

    To find once again for x all you need to do is divide all the six answers that was found in the 3rd revolution by 3, ensuring that it now lies in the domain \frac {\pi}{2}<x<\pi .
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