People who believe in biorhythms claim there are three cycle

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

E=sin(pi/2)t

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

a). Find E corresponding to t=6, 12, 18, 24, and 30. Describe what you observe.

b). What is the period of the emotional cycle?

Solution

a) E = sin(pie/2)*t

t = 6 , E = sin(180/2)*6

E = sin 540 = 0

t = 12, E = sin( 180/2)*12

E = 0

t = 18 , E = sin(180/2)*18

E = 0

t = 24 E = sin(180/2)*24

E = 0

t = 30 E = sin(180/2)*30

E = 0
which denotes neither emotionally high nor low

b) E = sin(pie/2)*t -----------------------------------------------------------1

in general E = sin (wt)

so by comparing , w = pie/2

2*pie / T = pie / 2

T ( time period ) = 4 days