Thread: 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.

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.

Does that help you?

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.

your equation has the form



where

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

B = the period, where

and C = the vertical translation

If you wave wavelength is 6 then,

and

I hope that helps some.