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Math Help - trig equation help

  1. #1
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    trig equation help

    Solve in the interval  0\leq x \leq 2\pi ,

     cosec(x + \frac{\pi}{15} ) = -\sqrt{2}

    not really sure what to do,

    I expanded the brackets and got

     cosecx + cosec\frac{\pi}{15} = -\sqrt{2}

    anything I try from here just gives me very wrong answers, can anyone suggest what I do next?

    thank you.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Tweety View Post
    Solve in the interval  0\leq x \leq 2\pi ,

     cosec(x + \frac{\pi}{15} ) = -\sqrt{2}

    not really sure what to do,

    I expanded the brackets and got

     cosecx + cosec\frac{\pi}{15} = -\sqrt{2}

    anything I try from here just gives me very wrong answers, can anyone suggest what I do next?

    thank you.
    You don't expand trig functions like that.

    \frac{1}{sin\left(x+\frac{\pi}{15}\right)} = -\sqrt{2}

    Take the reciprocal.

    sin\left(x+\frac{\pi}{15}\right) = -\frac{1}{\sqrt2}

    \left(x+\frac{\pi}{15}\right) = arcsin\left(-\frac{\1}{\sqrt2}\right)
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