Graph the function \(y = 2\sin(x - \frac{\pi}{3})\).
Answer
Finally, make sure the graph repeats every \(2\pi\) units, which represents the period of 2.
Step 1 ：First, identify the amplitude, period, phase shift, and vertical shift from the equation. Here, the amplitude is 2, the period is \(2\pi\), the phase shift is \(\frac{\pi}{3}\) to the right, and there is no vertical shift.
Step 2 ：Next, draw a rough sketch of the basic sine function, \(y = \sin(x)\), on an interval from 0 to \(2\pi\).
Step 3 ：Now, amplify the graph by a factor of 2 to represent the amplitude. This means all y-values on the graph are multiplied by 2.
Step 4 ：Then, shift the graph to the right by \(\frac{\pi}{3}\) units to represent the phase shift.
Step 5 ：Finally, make sure the graph repeats every \(2\pi\) units, which represents the period of 2.
