# Properties and Graph of the Function y=cot(x)

Properties are following:

1. Domain is x!=pik,k in Z (in other words function is not defined for those values of x where sin(x)=0).
2. Range is all number line.
3. Function is periodic with main period pi.
4. Function is odd.
5. Function is increasing on intervals [pik,pi+pik],k in Z.
6. Lines x=pik,k in Z are vertical asymptotes.

Let's first draw graph on the interval (0,pi/2]. Find some values of function:

• if x=pi/4 then y=cot(pi/4)=1;
• if x=pi/3 then y=cot(pi/3)=sqrt(3);
• if x=pi/2 then y=cot(pi/2)=0.

Draw these points and connect them with smooth line. We've obtained graph of the functon on interval (0,pi/2].

Since y=cot(x) is odd, then draw part of the graph symmetric about origin to the graph on interval (0,pi/2]. We've obtained graph of the function on interval [-pi/2,pi/2].

Now, using the fact that cotangent is periodic with period pi we can draw graph of the function on all domain.