Why is tan x an odd function

4. Function y = tan x and its properties

The function is well-defined, is an odd and periodic function with a period.
Because of these properties, it is sufficient to create the graph in the interval.
For the creation of the graph we choose those points whose coordinates we already know:
 
By representing them point-symmetrically to the origin, one obtains the graph in the interval.
With the help of the periodicity one then creates the graph of the function \ (y = tan x \) in the entire definition range.
Features of the function
1. The domain of the function is the set of all real numbers.
2. The range of values ​​is the set of all real numbers.
3. The function is periodic with period.
4. The function is an odd function.
5. The function takes:
- the value \ (0 \) if.
- positive values ​​in the intervals.
- negative values ​​in the intervals.
6. The function increases in the intervals