Write a sine function that has an amplitude of 4, a midline of y=3 and a period of 8/7.
The general form of a sine function is given by:
y = A sin(Bx+C) + D
where
A = amplitude
B = 2π/period
C = phase shift
D = vertical shift (midline)
Given the information provided:
Amplitude (A) = 4
Midline (D) = 3
Period (P) = 8/7
To find B, we plug in the period value into B = 2π/period:
B = 2π/(8/7) = 7π/4
Therefore, the equation of the sine function is:
y = 4 sin((7π/4)x + C) + 3
The phase shift (C) is not given, so we assume it to be zero for simplicity. If a specific phase shift is desired, it needs to be specified.
Thus, the final equation is:
y = 4 sin((7π/4)x) + 3