Question

Help confused with applying sine and cosine functions

Answer 1

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. During the first cycle of breathing, when will the air flow be at its maximum and what will the air flow be at that point in time?

Answer 2

everyone tells me to solve for the derivative and I have not learned that being in precal s:

Answer 3

@Directrix

Answer 4

@DarkBlueChocobo

I took the function over to Desmos.com and graphed it.

y = .6 * sin (( 2π/5)*x)

You can read what you want to know right off the graph. Just put the cursor or stylus on the first positive x for a maximum and click. You'll see the coordinates.

Answer 5

so the maximum is 1.25,0.6?

Answer 6

@Directrix

Answer 7

x is the time at which the maximum volume of liters per second will be reached.

Answer 8

To just say this >>> so the maximum is 1.25,0.6?

is not correct because an ordered pair is not a maximum.

Pull the ordered pair apart to get the time and the maximum

Answer 9

the airflow will be at its maximum at 1.25 and the air flow is at .6

Answer 10

@Directrix

Answer 11

1.25 seconds*

Answer 12

The maximum velocity of the intake air is not measured in seconds.

>>, where x is measured in seconds.

Answer 13

This is backwards: the airflow will be at its maximum at 1.25 and the air flow is at .6

Answer 14

liters per second oops and so the air flow will be at its maximum at .6 and the air flow is at 1.25 L/s?

Answer 15

I just need to look at it more to see that the max would be .6 ._. because range and 1.25 is the domain *facepalms*

Answer 16

so the air flow will be at its maximum at .6 seconds at which time the air flow is at 1.25 L/s?

Answer 17

^^ Correct

Answer 18

@DarkBlueChocobo

Answer 19

Lel Yeh i saw that too late lool, but how would you find out the exact second?

Answer 20

i read it off the graph.

Answer 21

Think about the sine function. The biggest value the sine of an angle can ever be in its life is 1.

Answer 22

Question though didn't we answer the question at hand though because we found the maximum and the air flow

Answer 23

We did answer the question at hand from the graph.

I am now trying to tell you how to answer the question without a graph and without using derivatives from Calculus.

Answer 24

Ohh ok so with what you said would that mean it would be 1 second then?

Answer 25

1 second? I did not say anything about one second.
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You have time, air flow, and maximum mixed up in your head.

When you sort that out, then I'll come back and tell you another way to do this problem.

Answer 26

Alright

Answer 27

So the time is what x equals. The air flow and maximum is what are looking for. The air flow is the domain and the maximum is the range

Answer 28

@Directrix would this look right then?

Answer 29

>>> So the time is what x equals. The air flow and maximum is what are looking for. The air flow is the domain and the maximum is the range

No.

Answer 30

>>>So the time is what x equals. Yes.

Answer 31

The air flow is what y equals.

Answer 32

The TIME (x) at which the air flow was a maximum is what are looking for.

Answer 33

ohhh so that means that 1.25 is the time for this problem?

Answer 34

x = .6 seconds is the time for this problem.