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]`.graph of the function y=cos(x)

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.