# finding a trig equation from graph

• Apr 29th 2009, 12:07 PM
winegum66
finding a trig equation from graph
I have a graph, the maximum value is 36, the minimum value is 4 and it cycles every 6 hours. So at time = 0 the graph is at 4 on the y axis, then at time 6 it is at 36, 12 it is at 4 hours, and so on. So the points are (0,4), (6,36), (12,4) etc. I have to find the equation for this graph using a transformation of y = sin(x). So far I have y = 32sin(π/9 t) + 4, but everytime i run this on a graphing simulator the results go into the negative values so i am sure it is wrong I'm really stuck here, and it is quite frustrating, can anyone help. thank you.
• Apr 29th 2009, 02:59 PM
VonNemo19
Maybe this'll help.
Try to "center" your equation first by assuming that its max and min are equidistant from the x-axis. Like this:

36-4=32 and if i center,then it s max and min are both 16 units from the x-axis.

Now i figure out the equation, and then I add to the right side of the equation whatever I must in order to make it shift up the graph.

• Apr 29th 2009, 07:35 PM
winegum66
I sorta know what you mean, it was what i was trying to do, but i still get the wrong graph, it is driving me nuts.
• Apr 29th 2009, 08:04 PM
pickslides

$\displaystyle y = Asin(nt) + C$

where

A = the amplitude = (max - min)/2 = (36-4)/2 = 16

B = the period, where $\displaystyle B = \frac{2\pi}{n}$

and C = the vertical translation

If you wave wavelength is 6 then, $\displaystyle 6 = \frac{2\pi}{n}$

and $\displaystyle n = \frac{\pi}{3}$

I hope that helps some.