In a sinusoidal model of the form y = #a*sin(b(x - c))+d#, the period is found by taking #(2*pi)/|b|#. Frequency is the reciprocal of period.
Example: y = #2*sin(3x)# would have a period of #(2pi)/3#, which is one-third the length of the "normal" period of #2pi#. Another way to describe this change from the Parent function would be to say that the graph would cycle through 3 times by the time it reaches #2pi#. The frequency looks like it is directly affected by the value of "b" in this equation, which is 3.
Now, make a prediction yourself. What is the frequency of the graph of y = #-1/4*sin((1/2)x)+1#?
Answer: The period would be #(2pi)/(1/2)# or #4pi#, which is twice as long as the Parent function. The frequency would be #1/(4pi)#, which is difficult to interpret. If the period is DOUBLED, then the frequency is cut in half. You will only see HALF of a cycle by the time you reach #2pi# in this case.
