Properties and Graph of the Function y=cos(x)
Properties are following:
- Domain is all number line.
- Range is segment `[-1,1]`.
- Function is periodic with main period `2pi`.
- Function is even.
- 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.