What would be the axis of the curve for f(x)=sinx and f(x)=cosx?

Answer 1

Both sine and cosine functions oscillate around what is sometimes called the sinusoidal axis. More commonly, this is called the midline (however I've also heard it called the principal axis). Here is a sketch:

As you can see, this midline is the x-axis or y = 0

Answer 2

Both are symmetric about the x axis.