max = 5, min = -1
mid = (5-1)/2 = 2
{observe for sinx,
max = 1, min, = -1, mid=0}
since mid=2 we can let the function
y=a•sin(bx+c)+2
2a=max-min=6
a=3
y=3sin(bx+c)+2
the graph cross (0,2) so
2=3sin(c)+2
3sin(c)=0
c=0 or c=π
since the graph go down after (0,2), then we choose c=π.
max=5 with x=-1, so
5=3sin(-b+π)+2
sin(-b+π)=1
b=π/2
at last the get the exact equation, that's
[tex]y = 3sin( \frac{\pi}{2} x + \pi) + 2[/tex]
