# Sine & Cosine Wave Function World Problem

• Apr 1st 2009, 09:20 PM
realintegerz
Sine & Cosine Wave Function World Problem
So, we've been doing these lately in my intro to calc class, and I'm not getting them at all, I get normal displacement and stuff but when it comes to relating it to a word problem they make me (Headbang).

When a person is breathing normally, the amount of air in their lungs varies sinusoidally. When full, Karen's lungs hold 2.8 liters of air. When empty, her lungs hold 0.6 liters of air. Her brother starts timing her breathing. At t = 2 seconds she has exhaled completely and at t = 5 seconds she has inhaled completely. Find an EQ that will model the amount of air in Karen's lungs at any time, assuming she breathes normally.

All I know, or want to assume, is that in 3 seconds she exhale and inhales, that's all I understand..

a) Find the amount of air in Karen's lungs if she starts holding her breath 3.5 seconds into the timing.

b) Find the first time that Karen has 2.3 liters of air in her lungs
• Apr 2nd 2009, 04:02 AM
HallsofIvy
Quote:

Originally Posted by realintegerz
So, we've been doing these lately in my intro to calc class, and I'm not getting them at all, I get normal displacement and stuff but when it comes to relating it to a word problem they make me (Headbang).

When a person is breathing normally, the amount of air in their lungs varies sinusoidally. When full, Karen's lungs hold 2.8 liters of air. When empty, her lungs hold 0.6 liters of air. Her brother starts timing her breathing. At t = 2 seconds she has exhaled completely and at t = 5 seconds she has inhaled completely. Find an EQ that will model the amount of air in Karen's lungs at any time, assuming she breathes normally.

All I know, or want to assume, is that in 3 seconds she exhale and inhales, that's all I understand..

Well, that's not what I understand! It looks to me like she take 5 seconds to "exhale and inhale". It takes her 2 seconds to exhale and 3 seconds to inhale.

Quote:

a) Find the amount of air in Karen's lungs if she starts holding her breath 3.5 seconds into the timing.
Since the time from 2.8 liters to 0.6 liters in her lungs is 2 seconds but the time from 0.6 liters to 2.8 liters is 3 seconds, I don't see how this can be "sinusoidal". Are you sure you have the right numbers?

Quote:

b) Find the first time that Karen has 2.3 liters of air in her lungs