# Domain question.

• Feb 23rd 2010, 02:09 AM
Stroodle
Domain question.
Hi, I'm having a little trouble understanding how the domain of trig problems work. For example:

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

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

• Feb 23rd 2010, 02:18 AM
mr fantastic
Quote:

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

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

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