Amplitude is 4, Midline is 0, Period is 8 pi. No phase or horizontal shifts. Find b.
In an equation of the form y = a sin(bx+c) + d, the amplitude is given by |a| and the midline is given by d. Since the amplitude is 4 and the midline is 0, we have |a| = 4 and d = 0.
The period of the function is given by P = 2π/|b|. We are given that the period is 8π, so we set up the equation:
8π = 2π/|b|
Dividing both sides of the equation by 2π, we get:
4 = 1/|b|
Taking the reciprocal of both sides, we have:
1/4 = |b|
Since b cannot be negative (as there is no reflection), we have b = 1/4.
Therefore, b = 1/4.