Well here it is:
period of y=2 cos(1/4x)
I realize this much: T=2pi/w=2pi/1/4=8pi
Is that correct? Is it 8pi ?
Let's ignore the pi part for a minute.
Draw a line segment.
Label one endpoint "0" and the other endpoint "8" (to represent a segment of length eight)
Label the midpoint "4"
Label the midpoints of the smaller segments - "2" and "6".
Now copy this onto your x-axis and add "pi" after each x-coordinate!