Fundamental Trigonometry

[tkhunny]

A user named "helpless" posted this question privately. I though hwlpless should share...

I was wondering if you could help me with my calculus problem
i got a table of values..
2 16.40
3 15.70
4 15.30
5 15.20
6 15.21
7 15.40
8 15.80
9 16.30
10 16.80
11 17.50
12 18.18
13 18.70
14 19.36
15 19.88
16 20.40
17 20.85
18 21.22
19 21.60
20 21.65
and i was supposed to graph it. i did it and i got a wierd curve, next i had to figure out an equation that would fit that curve...but i have no idea how to do it. I found an equation on excel, but it doesnt fit the curve..im really lost....
can you please help me solve it?

I sincerely hope you posted this publicly, rather than waiting for me for three days.

A quick look suggests f(x) = sin(x), except

Amplitude = (Max - Min)/2 = (21.65 - 15.2)/2 = 3.225

Now we have f(x) = 3.225*sin(x), except

Center = (Max + Min)/2 = (21.65 + 15.2)/2 = 18.425

Now we have f(x) = 18.425 + 3.225*sin(x), except

Period = (xmax - xmin)*2 = (20 - 5)*2 = 15*2 = 30

Now we have f(x) = 18.425 + 3.225*sin((2pi/30)*x), except

Zero = (zmax + zmin)/2 = (20+5)/2 = 25/2 = 12.5

Now we have f(x) = 18.425 + 3.225*sin((2pi/30)*(x-12.5)), except

Nothing! That's pretty much it.

You must know the parameters and what they do. You CAN be expected to do this on an exam.

 

[fasteddie65]

Plotting the points it does look sinusoidal. Using a sine regression on my TI-84, I found the following equation:
y = 3.15sin(0.22x - 2.75) + 18.43, to the nearest hundredth.

 

[tkhunny]

1) What will you do when your batteries die?

2) So, what you are saying is that the original solution was pretty good for pencil and paper.

Having a clue how things work substitutes for much technology. Technology will continue to struggle mightily with trying to replace having a clue how things work.