91Ó°ÊÓ

Biorhythms In the theory of biorhythms, a sine function of the form

$P\left(t\right)=50\sin \left(\mathrm{Ó\neg }t\right)+50$

is used to measure the percent P of a person's potential at time t, where t is measured in days and$t=0$ is the person's birthday. Three characteristics are commonly measured:
Physical potential: period of 23 days
Emotional potential: period of 28 days
Intellectual potential: period of 33 days
(a) Find$\mathrm{Ó\neg }$ for each characteristic.
(b) Using a graphing utility, graph all three functions on the same screen.
(c) Is there a time t when all three characteristics have$100\%$ potential? When is it?
(d) Suppose that you are 20 years old today $(t=7305days)$. Describe your physical, emotional, and intellectual potential for the next 30 days.