the frequency is 1 divided by the period.
in a normal cycle, the period is equal to 2p/1 = 2p
p is equal to pi which is equal to 3.141592654
here's a graph of y = sin(x).
the amplitude is equal to 1
the period is equal to 2p which is equal to 6.28....
here's a graph of y = 3sin((p/2)x).
the amplitude is equal to 3.
the period is equal to 4.
the period is the length of one full cycle. at the end of a full cycle, the pattern starts repeating itself again.
the frequency is the number of times the pattern repeats itself within a normal cycle of 360 degrees which is equal to 2p.
in your example, the period is equal to 4.
the frequency is 1 / period = 1/4.
this means that the full cycle will be shown 2p/4 = 1.57 times in a normal period of 2p.
to describe this further, the graph of y = sin(x) has a period of 2p and a frequency of 1/2p.
the frequency means that the full cycle will be shown 1/2p * 2p = 1 time in a normal period of 2p.
to go one step further, the graph of y = sin(2x) has a period of p.
it's frequency is 1/p.
the frequency means that the full cycle will be shown 1/p * 2p = 2 times in a normal period of 2p.
when you graph the function, the period is the length along the x axis which is described in terms of radians rather than degrees.
1 normal cycle would be 6.28 in length on the graph.
your function was equal to 4 in length on the graph.
here's a reference you might want to check out.
http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_trigperiodfreq.xml