Chapter 4.5, Problem 79E

Respiratory Cycle For a person exercising, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is modeled by

$v=1.75\sin \left(\pi t/2\right)$

Where t is the time (in seconds). (Inhalation occurs when $v>0$, and exhalation occurs when $v<0.)$

(a) Find the time for one full respiratory cycle.

(b) Find the number of cycles per minute.

(c) Sketch the graph of the velocity function.