Chapter 1.5, Problem 80E

For a person at rest, 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 $v=0.85\text{ sin}\left(\pi t/3\right),$ where $t$ is the time (in seconds).

$\left(\text{a}\right)$ Find the time for one full respiratory cycle.

$\left(\text{b}\right)$ Find the number of cycles per minute.

$\left(\text{c}\right)$ Sketch the graph of the velocity function. Use the graph to confirm your answer in part  $\left(\text{a}\right)$ by finding two times when new breaths begin. (Inhalation occurs when $v>0$, and exhalation occurs when $v<0$.)