the midline is at (36+81)/2=58.5 this is the vertical shift(d)
amplitude (a) is the distance from the midline to the peak or trough 58.5-36= 22.5
period is 12 (trough to peak is 6 and another 6 to complete the cycle back to trough)
b is (2pi)/12= pi/6
Since you start at your minimum value this would be a negative cosine graph.
There is a phase shift of 1 to the right ( graph starts at x=1 instead of x=0)
equation is y =-22.5cos(pi/6)(x-1) +58.5
Stephen K.
tutor
I hope you have drawn the original graph. It ALWAYS helps to draw a picture or graph for geometry and trig. problems. Anyway sine starts at the midline which is at x=4 so you now have a positive sine graph with a phase shift of 4 .
y= 22.5sin[(pi/6)(x-4)] +58.5. If you graph this in desmos you will see it is exactly the same as the -cosine graph.
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11/08/20
Grace M.
thank you SO much! what would the sin equation be?11/08/20