1. ## 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??

2. Originally Posted by Stroodle
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??