To write the equation of the sine function with the given parameters, we'll use the general form of the equation:
y = A * sin(B(x - C)) + D,
where:
A is the amplitude,
B determines the period,
C is the phase shift, and
D is the vertical shift.
In this case, the given parameters are:
Amplitude (A) = 1/7,
Period (B) = 2Ï€,
Phase shift (C) = 6Ï€, and
Vertical shift (D) = 10.
Using these values, we can substitute them into the equation:
y = (1/7) * sin(2Ï€ (x - 6Ï€)) + 10.
Simplifying further:
y = (1/7) * sin(2πx - 12π²) + 10.
Therefore, the equation of the sine function with an amplitude of 1/7, a period of 2Ï€, a phase shift of 6Ï€, and a vertical shift of 10 units up is:
y = (1/7) * sin(2πx - 12π²) + 10.