Question

A sinusoid (sine curve) rises from a minimum value of y=-8 at x=0 to a maximum value of y=40 at x=50. Write a sine function for this curve

Answer 1

The function has a mean value of (40-8)/2 = 16 (which will have to be added as a constant term), and it attains the mean value when x = 25. The amplitude is 40-16 - 24. Since is goes from min to max when x changes by 50, the period is 100

F(x) = 16 + 24 sin[2 pi (x-25)/100]
= 16 + 24 sin[pi(x-25)/50]