Expert: Chanda Walker - 2/23/2009

Question
Chanda,
I am asking this just in cast you possibly know the answer.

Question:

People who believe in biorhythms clam that there are three cycles that rule our behavior-the physical, emotional, and mental. Each is a sine functions of a certain period. The function for our emotional fluctuations is:

                E = sin pi/14 t

where t measured in days starting at birth. Emotional fluctuations,E, are measured from -1 to 1, inclusive, with 1 representing peak emotional well-being, -1 representing the low for emotional well-being, and 0 representing feeling neither emotionally high nor low.

1.  Find E corresponding to t = 7,14,21,28, and 35. Describe what you observe.

2.  What is the period of the emotional cycle in days?

Answer
This problem is essentially a math problem so I can help but I have no expertise biorythyms.  (Does anyone?)

Ok the problem.

E = sin ( Pi/14  * t)

E = Sin ( Pi * 7/14) = Sin(Pi/2) = 1

E = Sin ( Pi * 14/14) = Sin(Pi) = 0

E = Sin ( Pi * 21/14) = Sin(3*Pi/2) = -1

E = Sin ( Pi * 28/14) = Sin(2*Pi) = 0

E = Sin ( Pi * 35/14) = Sin(5 Pi/2)= Sin (Pi/2) = 1

The mood is cyclical.  Each week the mood moves through 1/4 of the cycle.

In general a sin wave is given in this form:

sin( 2* Pi * t) where 1 is the period.  If we rewrite this equation we find:

sin( 2* Pi* (t/28))

That means the period of the emotional cycle is 28 days.