people who believe in biorhythms claim there are three cycles that rule our behavior - the physical…

people who believe in biorhythms claim there are three cycles that rule our behavior - the physical, emotional, and mental. each is a sine function of a certain period. the function for our emotional fluctuations is e = sin(\\frac{\\pi}{10}t) (equation may not be based on actual studies.) 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 = 5, 10, 15, 20, and 25. describe what you observe. b. what is the period of the emotional cycle? a. find e corresponding to t = 5. e =

people who believe in biorhythms claim there are three cycles that rule our behavior - the physical, emotional, and mental. each is a sine function of a certain period. the function for our emotional fluctuations is e = sin(\\frac{\\pi}{10}t) (equation may not be based on actual studies.) 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 = 5, 10, 15, 20, and 25. describe what you observe. b. what is the period of the emotional cycle? a. find e corresponding to t = 5. e =

Answer

Explanation:

Step1: Substitute t = 5 into the formula

Substitute (t = 5) into (E=\sin\frac{\pi}{10}t). So (E=\sin(\frac{\pi}{10}\times5)=\sin\frac{\pi}{2}).

Step2: Evaluate the sine - value

We know that (\sin\frac{\pi}{2}=1).

Step3: Substitute t = 10 into the formula

Substitute (t = 10) into (E = \sin\frac{\pi}{10}t). Then (E=\sin(\frac{\pi}{10}\times10)=\sin\pi). Since (\sin\pi = 0).

Step4: Substitute t = 15 into the formula

Substitute (t = 15) into (E=\sin\frac{\pi}{10}t). So (E=\sin(\frac{\pi}{10}\times15)=\sin\frac{3\pi}{2}). And (\sin\frac{3\pi}{2}=- 1).

Step5: Substitute t = 20 into the formula

Substitute (t = 20) into (E=\sin\frac{\pi}{10}t). Then (E=\sin(\frac{\pi}{10}\times20)=\sin2\pi). Since (\sin2\pi = 0).

Step6: Substitute t = 25 into the formula

Substitute (t = 25) into (E=\sin\frac{\pi}{10}t). So (E=\sin(\frac{\pi}{10}\times25)=\sin\frac{5\pi}{2}). And (\sin\frac{5\pi}{2}=1).

Observation: The emotional - well - being value (E) oscillates between 1, 0, and - 1 as (t) increases.

Step7: Find the period of the function

For a sine function of the form (y = A\sin(Bx - C)+D), the period (T) is given by (T=\frac{2\pi}{B}). In the function (E=\sin\frac{\pi}{10}t), (B = \frac{\pi}{10}). Then (T=\frac{2\pi}{\frac{\pi}{10}}).

Step8: Simplify the period formula

(T=\frac{2\pi}{\frac{\pi}{10}}=2\pi\times\frac{10}{\pi}=20).

Answer:

a. When (t = 5), (E = 1); when (t = 10), (E = 0); when (t = 15), (E=-1); when (t = 20), (E = 0); when (t = 25), (E = 1). We observe that the value of (E) oscillates between 1, 0, and - 1 as (t) increases. b. The period of the emotional cycle is 20 days.