Answer: The general form of a sine function is y = A sin(Bx + C) + D, where A is the amplitude, B is the coefficient of x that determines the period (B = 2π/period), C is the phase shift, and D is the vertical shift.
In this case, the amplitude is given as 8 and the period is given as 6x. Therefore, we can write:
A = 8
period = 6x
Using the formula B = 2π/period, we can find the value of B:
B = 2π/(6x) = π/x
Since we want the function to be in the form y = Asin(x) or y = Acos(x), we can choose to write the sine function as:
y = A sin(Bx)
Substituting the values of A and B, we get:
y = 8 sin(πx/6)
Therefore, the equation of the sine function with amplitude 8 and period 6x is:
y = 8 sin(πx/6)
hope it helps!!