The function fx = 4 sin(2x) + 5 can be analyzed to determine its amplitude, period, and phase shift.
Amplitude
The amplitude of a sine function in the form y = A sin(Bx + C) + D is given by the absolute value of A. In this case, A = 4, so the amplitude is 4. This means that the wave oscillates 4 units above and below its midline.
Period
The period of a sine function is calculated using the formula Period = (2π) / |B|. Here, B = 2, so the period is (2π) / 2 = π. This indicates that the function completes one full cycle every π units along the x-axis.
Phase Shift
Finally, the phase shift can be analyzed using the term C in the function, but since there is no horizontal shift explicitly present in the equation (i.e., there is no term like + or – inside the sine function), the phase shift is 0. This means the function starts at the origin without any left or right displacement.
In summary:
- Amplitude: 4
- Period: π
- Phase Shift: 0