Determine an equation of a sinusoidal function that has a maximum at (5, 4)

Question

and a minimum at (2, -10).

Answer 1

amplitude = (max-min)/2 = 7
center of wave is at y = (max+min)/2 = -3

f(x) = 7cos(ax+b) - 3

since min is at x=2, and the half-period is 5-2 = 3, the period is 6.

f(x) = -7cos(π/3(x-2))-3