Write the equation of the sine function with an amplitude of 1/7, a period of 2pi, a phase shift of 6pi, and a vertical shift of 10 units up ?
you should be familiar with the general equation of a sine function for the above problem.
Just insert the values, the only value needing any consideration is the period
period = 2π/k, k = 2π/(2π) = 1
so
y = (1/7) sin 1(Ø - 6π) + 10 or
y = (1/7) sin(Ø - 6π) + 10
To write the equation of a sine function with the given parameters:
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) = 2π
Phase Shift (C) = 6π
Vertical Shift (D) = 10
Substituting the values into the general form equation:
y = (1/7) sin((2π)(x - 6π)) + 10
Simplifying:
y = (1/7) sin(2πx - 12π) + 10
Thus, the equation of the sine function with an amplitude of 1/7, a period of 2π, a phase shift of 6π, and a vertical shift of 10 units up is:
y = (1/7) sin(2πx - 12π) + 10
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) = 2π,
Phase shift (C) = 6π, and
Vertical shift (D) = 10.
Using these values, we can substitute them into the equation:
y = (1/7) * sin(2π (x - 6π)) + 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 2π, a phase shift of 6π, and a vertical shift of 10 units up is:
y = (1/7) * sin(2πx - 12π²) + 10.