Question

I need this explained and all work shown. (Questions attached). Medal and fan for best answer :)

Answer 1

set that mess on the inside equal to \(\frac{\pi}{2}\) and solve for \(m\)

Answer 2

You have the function \(a(m)\) and you want to maximize it. Think about when the \(\sin\) function is at its highest.

Answer 3

I don't understand what that means? @satellite73

Answer 4

Take a look at the unit circle. What is the highest possible value for \(\sin\), and at what angle does this occur?

Answer 5

90 degrees? @dummyguy

Answer 6

Yes. What is 90 degrees in radians (in terms of \(\pi\))?

Answer 7

So its \[\pi \div 2\] right?

Answer 8

Yes, at \(\frac{\pi}{2}\), the \(\sin \) function is at its highest.

Note that \(a(m)=30\sin(\frac{m \pi}{5} + \frac{3\pi}{10})\) is sinusoidal wave, but it is just a scaled version of the \(\sin\) function we all know and love.

So would you agree that \(a(m)\) ranges between \([-30,30]\)?

Answer 9

No matter what we stick inside the \(\sin\) portion of \(a(m)\), we will have a value between the values of \(-30\) and \(30\).

Answer 10

That makes sense, I need to answer in minutes though, and show my work. I'm not exactly sure how to write out what you just did

Answer 11

Okay, so using what you know about \(a(m)\) and \(\sin\), what's the highest possible value of \(a(m)\) and at what angle will this value occur?

Answer 12

I'm guessing that the new highest value of sin is 30? and that the angle will be..actually I have no idea what I'm talking about. @dummyguy

Answer 13

You are on the right path and indeed have an idea of what you are talking about :). That is the maximum value! So the brain activity is highest when \(a(m) = 30\)... hmm.

\(30\sin(\frac{m\pi}{5}+\frac{3\pi}{10})=30\) when the function is highest. But that must mean that..

\(\sin(\frac{m\pi}{5}+\frac{3\pi}{10})=1\), right? What is the inside of \(\sin\) equal to when \(\sin\) is \(1\)?

Answer 14

Thanks for helping! And what do you mean by "inside of sine"

Answer 15

@dummyguy

Answer 16

\(\sin\) of what is \(1\)? And what does this tell you that \(\frac{m\pi}{5} + \frac{3\pi}{10}\) is equal to?

Answer 17

I know what this graph looks like on the calculator, I just am having trouble understanding how to correctly explain it. I know its 1, 30 and 11, 30

Answer 18

Avoid the calculator, it is not necessary for the problem. Let me recap what we have done so far:

-Realized we need to figure out what value of \(m\) gives us the maximum value for \(a(m)\).
-Recognized that \(a(m)\) is a sine function (as \(m\) ranges, \(a(m)\) oscillates).
-Before we look at what value of \(m\) gives us the highest value of \(a(m)\), we found what exactly this highest value is.

Now we need to solve for the \(m\) that gives us this desired maximum value (a.k.a \(30\)).

Answer 19

Okay, I think I understand all that, so I would plug 30 into m and then solve my equation? @dummyguy

Answer 20

Do you agree that 30 is the highest value that \(a(m)\)? This is because \(\sin\) ranges from \([-1,1]\). So \(30\sin\) ranges from \([-30,30]\), the highest value of which is \(30\).

But what you're looking for is the \(m\) that acheives this highest value.

Answer 21

In other words, you want \(30 = 30\sin(\frac{m\pi}{5}+\frac{3\pi}{10})\).

Answer 22

And you want to find the \(m\) that makes that true.

Answer 23

Okay, see that makes sense, but I contradict myself when I say I still don't get it as a whole, I'm kind of lost now. I know I've taken up a lot of your time, so you don't have to help me anymore. Thanks so much though.

Answer 24

@dummyguy

Answer 25

Tell me which part confuses you, and I'll help you.