since sin(kx) has period 2π/k, we need 2π/k = 3π
y = -3 + 4sin(2/3 x)
Write a sine function that has an amplitude of 4, period of 3π, and midline y = -3
2 answers
For the function f(x)=a*sin(bx+c)+d:
Amplitude: |a| -> |4| -> a
Period: 2pi/|b| -> 2pi/|b| = 3pi -> b=2/3
Phase shift: -c/b -> 0
Midline: y=d -> y=-3
Therefore, your sine function would be f(x)=4sin((2/3)x)-3
Amplitude: |a| -> |4| -> a
Period: 2pi/|b| -> 2pi/|b| = 3pi -> b=2/3
Phase shift: -c/b -> 0
Midline: y=d -> y=-3
Therefore, your sine function would be f(x)=4sin((2/3)x)-3