# What is the domain and range of y=tan x?

Oct 10, 2015

Domain: (theta|theta!=kpi/2, where k is an odd integer)
Range: $\left(- \infty , \infty\right)$

#### Explanation:

Remember that $\tan = \frac{\sin}{\cos}$ therefore, you will have a vertical asymptope whenever cos=0. Cos=0 every odd multiple of $\frac{\pi}{2}$.

If you plug y=tan(x) into a graphing calculator you will see that the ends of each section continue on infinitely along the y-axis.