Answer:
Explanation:
The general form of a sinusoidal function is given by:
y = A sin (Bx - C) + D
where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
Given: Amplitude = 2/3, Period = pi/4, Phase Shift = pi/6 units to the left
The amplitude is 2/3, which means that A = 2/3.
The period is pi/4, which means that one cycle of the function occurs over a distance of pi/4. We know that the period is related to the frequency by the formula:
Period = 2pi / B
Solving for B, we get:
B = 2pi / Period
B = 2pi / (pi/4)
B = 8
The phase shift is pi/6 units to the left, which means that C = pi/6.
Finally, there is no vertical shift in this case, so D = 0.
Putting it all together, we get:
y = (2/3) sin (8x - pi/6)