After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , where t is the time (in seconds) .
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )

Find the time for one full respiratory cycle.

Question

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0. )
​
Find the time for one full respiratory cycle.​
​
A)6 sec
B)2 sec
C)7 sec
D)3 sec
E)8 sec

Quizplus · Accepted Answer

The period of the sine function $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ is given by the formula $T = \frac{2\pi}{\omega}$, where $\omega$ is the coefficient of $t$ inside the sine function. Here, $\omega = \frac{\pi}{3}$, so $T = \frac{2\pi}{\pi/3} = 6$ seconds. This means one full respiratory cycle, including both inhalation and exhalation, takes 6 seconds.

After Exercising for a Few Minutes,a Person Has a Respiratory v=1.75sin⁡(πt3)v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)v=1.75sin(3πt​)

After Exercising for a Few Minutes,a Person Has a Respiratory $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$