Expert: Paul Klarreich - 1/20/2012

Question
after exercising for a few minutes, a person has a respiratory cycle for which the velocity of air flow is approximated by v=1.79 sin(pi t/2) , where t is 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

the subject is pre-cal and the topic is graphs of sine and cosine functions

Answer
Questioner:alexa
Country:California, United States

Question:

after exercising for a few minutes, a person has a respiratory cycle for which the velocity of air flow is approximated by v=1.79 sin(pi t/2) , where t is time in seconds. (Inhalation occurs when v>0 and exhalation occurs when v<0.)
a)find the time for one full respiratory cycle.

SET the argument,  pi t/2, equal to 2 pi, and solve for t.


b)find the number of cycles per minute.

SET a minute equal to 60 seconds (duh!) and divide.

c)sketch the graph of the velocity function

1. Draw a VERY STANDARD sine curve.
2. Stick the answer to (a) at the end, on the x-axis.
2A. Put some intermediate values at the half- and quarter-marks.
3. Stick  1.79 on the y-axis at the top, -1,79 on the bottom.

Done.