write the equation of a sine function whose amplitude: 2 period: π/2 phase shift: 2/3
y = 2sin(4(x-2/3))
+_3
To write the equation of a sine function with the given amplitude, period, and phase shift, we can use the general form:
y = A sin(B(x - C)) + D
Where:
A represents the amplitude
B represents the frequency (reciprocal of the period)
C represents the phase shift
D represents the vertical shift (if any)
Given:
Amplitude (A) = 2
Period (T) = π/2
Phase shift (C) = 2/3
To find frequency (B), we can use the formula B = 2π / T:
B = 2π / (π/2)
B = 4
Substituting the known values into the equation, we have:
y = 2 sin(4(x - 2/3)) + D
Since the vertical shift (D) is not specified, we can assume it to be zero. If there is a given vertical shift value, you can substitute it accordingly.
Therefore, the equation of the sine function with the given amplitude, period, and phase shift is:
y = 2 sin(4(x - 2/3))
To write the equation of a sine function with the given amplitude, period, and phase shift, we can use the general form of a sine function:
y = A * sin(B(x - C))
In this case, the given information is:
Amplitude (A) = 2
Period (P) = π/2
Phase Shift (C) = 2/3
To find the value of B, we can use the formula:
B = 2π/P
Substituting the given period:
B = 2π / (π/2) = 4
Now we have all the values to write the equation:
y = 2 * sin(4(x - 2/3))
This is the equation of a sine function with an amplitude of 2, a period of π/2, and a phase shift of 2/3.