Determine the amplitude and phase shift for y=-2sin(x+pi/3)
In the given equation, y = -2sin(x + π/3), the amplitude and phase shift can be determined as follows:
The general equation for a sinusoidal function is given by y = A*sin(B(x - C)) + D, where A is the amplitude, B determines the period, C represents the phase shift, and D is the vertical shift.
Comparing this general equation to the given equation y = -2sin(x + π/3), we can determine the amplitude and phase shift:
Amplitude (A) = -2
The amplitude of a sinusoidal function represents the maximum distance the function fluctuates from its midline. In this case, the amplitude is -2, suggesting that the graph oscillates vertically between -2 and +2 from the midline.
Phase Shift (C) = -π/3
The phase shift of a sinusoidal function represents the horizontal shift of the graph. In this case, the phase shift is -π/3, indicating that the graph is shifted to the right by π/3 units.
Thus, the amplitude is -2, and the phase shift is -π/3.