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anonymous
 one year ago
Can someone help me with determining the equation for a trig function? I'm aware of how to find the amplitude and period, i'm just confused with this graph!
anonymous
 one year ago
Can someone help me with determining the equation for a trig function? I'm aware of how to find the amplitude and period, i'm just confused with this graph!

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MTALHAHASSAN2
 one year ago
Best ResponseYou've already chosen the best response.0wait how can we find the amplitute

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's usually the "a", I know how to determine it by looking at an equation

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \text{amplitude} = \frac{mn}{2}\] m = largest y coordinate of a point on the curve n = smallest y coordinate of a point on the curve

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444532222391:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444532254763:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in this case it would be 2+4/2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the midline is found by averaging the two extreme values \[\Large D = \frac{m+n}{2}\] y = D is the equation of the midline dw:1444532397834:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444532428898:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1`the midline is 1` yes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for the period since the points aren't actually on the radians how would I calculate where it starts and where it ends?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1look at the peak that lies on the y axis this is when x = 0 the next peak over to the right is at x = pi so the period is pi  0 = pi = pi units

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm a little confused..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when x=0 y=2, is that the peak that you're talking about?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1see the attached image

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks! I got that. I'm just confused why we are subtracting the pi0. I thought the formula for period was 2pi/k

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you might be thinking of T = 2pi/B and that is useful when you have an equation of this form y = A*cos(Bx  C) + D

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I subtracted the x values to find the distance between them

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the absolute value is to ensure the distance is positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for this graph we don't need to use that form. We just find distance simply by finding out the x values from the y and subtract them from one another?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you can pick on any 2 neighboring peaks and do the same thing

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we can't use that form because we don't have the equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok! That's where I was confused at :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you might have learned how to pick apart y = A*cos(Bx  C) + D (eg find the amplitude to be A, etc) but now we're going in reverse: finding the key elements and using them to construct the equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so our equation would be y=3sin(x)1?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is y when x = 0 ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1but does plugging in x = 0 give y = 2 when you use y = 3*sin(x)  1 ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so that equation doesn't fit

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1let's try cos instead of sin

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if x = 0, does y = 2 for y = 3*cos(x)  1 ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep, ok how about if x = pi/2, does y = 4 like it should?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we know that cos(x)=1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1cos(pi/2) = 0 actually

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and 31=2, and 21=1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1recall that the period is pi units so T = pi Solve the equation T = 2pi/B for B to get... T = 2pi/B pi = 2pi/B B*pi = 2pi B = 2pi/pi B = 2 so the equation should be y = 3*cos(2x)  1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now if we try x = pi/2, then y = 3*cos(2x)  1 y = 3*cos(2*pi/2)  1 y = 3*cos(pi)  1 y = 3*(1)  1 y = 3  1 y = 4 and it fits

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm a little lost. Why are we using t=2pi/3?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The period is T = pi going from peak to peak is pi units across

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug T = pi into T = 2pi/B and solve for B to get B = 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1T = 2pi/B is the period formula If you know B, you can find the period T (or vice versa)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we just knew the T, but in order to find b we had to plug in pi for t

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and how did you know that y=4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just the point on the graph?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Yes the point (pi/2, 4) is on the graph Notice how in my work above I replaced x with pi/2 in the equation y = 3*cos(2x)  1 Then I evaluated/simplified to get y = 4. So that confirms the equation works for x = pi/2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh so you just replaced it to check to see if the equation that we wrote was correct.. makes sense. :) Thank you lots!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes I recommend you check x = pi as well. Make sure that the output is y = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks again :) You're a life saver! I honestly had a lot of trouble with this problem

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'm glad it's making sense now
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