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

Properties are following:

1. Domain is all number line.
2. Range is segment [-1,1].
3. Function is periodic with main period 2pi.
4. Function is even.
5. Function is decreasing on intervals [2pin,pi+2pin] and increasing on intervals [-pi+2pin,2pin],n in Z.

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

• if x=0 then y=cos(0)=1;
• if x=pi/3 then y=cos(pi/3)=1/2;
• if x=pi/2 then y=cos(pi/2)=0;
• if x=pi then y=cos(pi)=-1.

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

Since y=cos(x) is even, then draw part of the graph symmetric about y-axis to the graph on interval [0,pi]. We've obtained graph of the function on interval [-pi,pi].

Now, using the fact that cosine is periodic with period 2pi we can draw graph of the function on all domain.