now [tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}[/tex] so, if the cosine of the angle, ever becomes 0, the rational becomes undefined. so hmmm other than those points, the values the angle can take on are pretty much anything, positive or negative ones... and the cosine is 0 at [tex]\bf \frac{\pi }{2}\qquad \frac{3\pi }{2}\qquad \textit{on the range of }[0,2\pi ][/tex]
so.. one can say the domain of tangent, is all angles EXCEPT those where cosine turns to 0
[tex]\bf \{x|x\in \mathbb{R}; x\ne \frac{\pi }{2}\pm\pi n\}\qquad \textit{\underline{n} being an integer}[/tex]
