Question

Some help would be appreciated

What is the equation of the midline of the sinusoidal function?

Answer 1

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

`y = 3sin( (\pi)/(2) x + \pi) + 2`