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Thread: Domain question.

  1. #1
    Senior Member Stroodle's Avatar
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    Domain question.

    Hi, I'm having a little trouble understanding how the domain of trig problems work. For example:

    If $\displaystyle \tan(x)=2$ and $\displaystyle x\in\left [0,\frac{\pi}{2}\right ]$ find the exact value of $\displaystyle tan(2x)$

    Now I know how to solve this and get the answer $\displaystyle -\frac{4}{3}$, but I don't understand how the answer can have a negative value when $\displaystyle tan$ is positive in the first quadrant. I'm sure it must something to do with the $\displaystyle 2x$, and that I'm missing something really fundamental here??

    Thanks heaps for your help!
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Stroodle View Post
    Hi, I'm having a little trouble understanding how the domain of trig problems work. For example:

    If $\displaystyle \tan(x)=2$ and $\displaystyle x\in\left [0,\frac{\pi}{2}\right ]$ find the exact value of $\displaystyle tan(2x)$

    Now I know how to solve this and get the answer $\displaystyle -\frac{4}{3}$, but I don't understand how the answer can have a negative value when $\displaystyle tan$ is positive in the first quadrant. I'm sure it must something to do with the $\displaystyle 2x$, and that I'm missing something really fundamental here??

    Thanks heaps for your help!
    2x is in the second quadrant ....
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