Write the equation of the trigonometric graph. Amplitude is 4, Midline is 0, Period is 8 pi. No phase or horizontal shifts. b=1/4
The equation of the trigonometric graph can be written as:
y = A * sin(b(x - h)) + k
where A is the amplitude, h is the horizontal shift (phase shift), k is the vertical shift (midline), and b is the coefficient of x which affects the period.
Given the information provided:
Amplitude (A) = 4,
Midline (k) = 0,
Period = 8π (which is equal to 2π / b, since b determines the period)
Since there are no horizontal shifts, the horizontal shift (h) = 0.
And given b = 1/4, we can determine the period as follows:
8π = 2π / b
8π = 2π / (1/4)
8π = 2π * 4/1
8π = 8π
Therefore, the equation of the trigonometric graph is:
y = 4 * sin((1/4)x) + 0
Simplified as:
y = 4sin(x/4)