How do you write a function for a sinusoid?
My Probelm has a Max of (9pi/8,1)
and a Min of (3pi/8,-5)
x-distance between the min and the max
= 9π/8 - 3π/8 = 3π/4
so the period is 3π/2
2π/k = 3π/2
k = 2π/(3π/2) = 4/3
amplitude = 3 and the vertical shift must be -2
so let's start with
y = - 3sin (4/3) x - 2
check with Wolfram:
for a min: https://www.wolframalpha.com/input/?i=min+of+y+%3D+-+3sin+(4x%2F3)+-+2
let n = 0
for a max: https://www.wolframalpha.com/input/?i=max+of+y+%3D+-+3sin+(4x%2F3)+-+2
let n = 0