Help with applying cosine and sine functions

Question

darkbluechocobo · Answer

The function$$f(x)=.6\sin(x(\frac{ 2\pi }{ 5 }))$$ represents the velocity of air flow of normal breathing cycles, where x is measured in seconds. A cycle consists of inhaling, where air flow is positive, and exhaling where air flow is negative. The air flow is measured in liters per second. How long is one complete cycle and what will the airflow be in 150 seconds?

darkbluechocobo · Answer

would I just need to fill 150 to find what the airflow would be at 150 seconds?

adamaero · Answer

Maybe...breathing doesn't need direction, just constant velocity... One cycle I'm assuming is breathing in and out (like the sin wave:) http://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-zero-offset.png You may have to double your answer. I can't tell from how the question is worded...

zepdrix · Answer

For the second part of the question, yes Blue :) Just plug in 150 for x.

For the first part, recall how to find your period (cycle),$$\Large\rm period=\frac{2\pi}{b}$$And our b is this coefficient,

zepdrix · Answer

$$\Large\rm y=a \sin\left(b x\right)$$

zepdrix · Answer

It's the thing attached to the x.

darkbluechocobo · Answer

oh so we would phil put 2pi/(2pi/5)

darkbluechocobo · Answer

@zepdrix would the period be 5?

darkbluechocobo · Answer

and would the air flow=0

darkbluechocobo · Answer

@xapproachesinfinity could you check these please? also what does it mean by how long it lasts?

zepdrix · Answer

Period of 5? Yes.
Zero for your air flow after 150 seconds? Yes, good job!