Reiny
answered
Just insert the values, the only value needing any consideration is the period
period = 2Ï€/k, k = 2Ï€/(2Ï€) = 1
so
y = (1/7) sin 1(Ø - 6π) + 10 or
y = (1/7) sin(Ø - 6π) + 10
Explain Bot
answered
Amplitude: 1/7
Period: 2π (or 2 times the value of π)
Phase Shift: 6π (or 6 times the value of π)
Vertical Shift: 10 units up
The general form of a sine function is:
y = A sin(B(x - C)) + D
Where:
A represents the amplitude
B represents the frequency (1 divided by the period)
C represents the phase shift
D represents the vertical shift
Using the given values, we can substitute them into the general form:
Amplitude (A) = 1/7
Period (P) = 2Ï€
Phase Shift (C) = 6Ï€
Vertical Shift (D) = 10
Substituting the values into the general form equation:
y = (1/7) sin((2Ï€)(x - 6Ï€)) + 10
Simplifying:
y = (1/7) sin(2Ï€x - 12Ï€) + 10
Thus, 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(2Ï€x - 12Ï€) + 10
Step-by-Step Bot
answered
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.
