calculus max/min volume question The volume of air contained in the lungs of a certain athlete is modeled by the equation
$$v=361\sin(91\pi t) +899$$
where $t$ is time in minutes, and $v$ is volume in cubic centimeters.
What is the maximum possible volume of air in the athlete's lungs?
Maximum volume=        (in cubic centimeters)
What is the minimum possible volume of air in the athlete's lungs?
Minimum volume=       (in cubic centimeters)
How many breaths does the athlete take per minute?
I am very lost I have no idea on how to approach it any help would be appreciated
 A: 
What is the maximum possible volume of air in the athlete's lungs?

A sine wave's amplitude is increased by the multiplier a in the the equation:
$$ y=a*sin(x) $$
This is because a sine wave $y=sin(x)$ has a max amplitude of 1 and you are multiplying it by a.
A sine wave's amplitude is also increased when you add a c at the end like the following equation:
$$ y=sin(x)+c $$
This increases the amplitude of the whole sine wave by c, so now the max amplitude of the sine wave is $(1+c)$
Multiplication come before addition in the order of operations, so you end up with the equation $((1*a)+c)$ for the maximum amplitude of:
$$ y=a*sin(x)+c $$

What is the minimum possible volume of air in the athlete's lungs?

A sine wave has a minimum amplitude of -1, so the minimum amplitude of:
$$ y=a*sin(x) $$
is $((-1)*a)$
You are also adding to the sine wave like above, so you add c also, for the equation $(((-1)*a)+c)$ as the minimum amplitude of the equation:

How many breaths does the athlete take per minute?

b is the frequency of the sine wave of the following equation:
$$ y=sin(b*x) $$
This means that after $(2\pi)$ the sine wave will have gone one cycle (up, down, and back up to it's mid-line). Another way to put this is $(b\ \div (2\pi))$ cycles every time x increases by 1.
A: I think that you are getting lost in the number of terms in the equation.  It's actually a very straightforward question, wrapped in a formula that just makes it look hard.
Ask yourself, what is the minimum and maximum value of $\sin()$ of anything?  Since sine itself has a maximum and minimum, it actually doesn't matter what's inside it for min/max calculations, as long as it is continuous.  $\sin()$ goes from -1 to 1, period, so it will be at a minimum at -1 and at a maximum at 1.  Then calculate the volumes in each case.
Now, on the "breaths per minute", this is based on the inside of the $\sin()$ function.
