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 2 years ago
A sine wave is shown in the attachment. Approximate the point shown on the graph. The unlabelled xaxis is on the same units as the y.
 2 years ago
A sine wave is shown in the attachment. Approximate the point shown on the graph. The unlabelled xaxis is on the same units as the y.

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inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0This is a sine wave shifted down 3 units, with an amplitude five times that of the parent function, and a period of 4. Thus the equation of the function is f(x)=5 sin( (pi*x)/4)3 0=5 sin( (pi*x)/4)3 Then, the x coordinate is 3/5=sin((pi/4)x) (pi*x)/4=arcsin(3/5) X=(4arcsin(3/5))/pi My work. The last two lines are wrong because of the arcsin. Please explain to me how to determine the second intersection p and not the first intersection.

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.0what did you get for x?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Some value that was correct for the first intersection of the function and the x axis. However, I"m looking for point p...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I'm really just having trouble understanding how to find each solution in this problem, and not just the 0<x<pi/2 solution that the inverse trig functions yield.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Well, the first solution is basically what you did. To get the next one, you find the xcoordinate for when your function is 3 for the second time. So first, at x=0, f(x)=3. Second, at x=4, f(x)=3. Now, you can find the xcoordinate of that first xintercept with arcsin. Take that value, and call it r. Now, 4r is the xcoordinate of your second point.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0So I take advantage of the fact that the sine graph is symmetrical?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1That's what I would do in this case anyways. Once you get a more complex graph, I'd have to think about it some more.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Uh, what about trig equations?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0for 3c I have \(\large \cos^{1}(\cos(x))=\pi/3\)

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I mean I'm tempted to just cancel out the functions, but I know that's wrong.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1It's wrong because the functions are periodic. So \[\cos^{1}(\cos(x))=\cos^{1}(\cos(x+2\pi))\]So strictly speaking, it's not really an actual inverse.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Wait but since we take the arccos second, we can cancel them out right?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Even then, I don't think you can cancel them unless you're in a very restricted domain.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I mean, cos always has that range, so the arccos would always yield the defined number that came from cos?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1According to wolfram, that only works for \(1\le x\le1\)
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