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Math Help - Domain of a trig. function!

  1. #1
    Member javax's Avatar
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    Domain of a trig. function!

    Hi guys.
    I need help on finding the domain of this function:

    y = \sqrt{sin\frac{1}{x}}
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  2. #2
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    Hello, javax!

    A tricky one . . .


    I need help on finding the domain of this function:

    . . y \:= \:\sqrt{\sin\frac{1}{x}}

    We see that: . \sin\frac{1}{x} \,\geq\,0

    This happens when \frac{1}{x} is on the intervals:

    . . \hdots\;(-4\pi,-3\pi),\;(-2\pi,-\pi),\;(0,\pi),\;(2\pi,3\pi),\;(4\pi,5\pi),\;\hdot  s

    That is: . 2n+1)\pi\;\text{ for any integer }n " alt="2n\pi \:\leq\:\frac{1}{x} \:\leq\2n+1)\pi\;\text{ for any integer }n " />


    Therefore: . \frac{1}{(2n+1)\pi} \;\leq \;x \;\leq \; \frac{1}{2n\pi}


    (I'll let you explain what happens when n = 0.)

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