1. **State the problem:** We want to graph the function $$y=2\sin\left(x-\frac{2\pi}{3}\right)-3$$. 2. **Formula and explanation:** This is a sinusoidal function of the form $$y=A\sin(B(x-C))+D$$ where: - $A=2$ is the amplitude (height of peaks). - $B=1$ controls the period (length of one cycle). - $C=\frac{2\pi}{3}$ is the horizontal phase shift. - $D=-3$ is the vertical shift. 3. **Period calculation:** The period is given by $$\frac{2\pi}{|B|} = \frac{2\pi}{1} = 2\pi$$. 4. **Phase shift:** The graph shifts right by $$\frac{2\pi}{3}$$ units. 5. **Amplitude and vertical shift:** The graph oscillates between $$-3-2=-5$$ and $$-3+2=-1$$. 6. **Summary:** The sine wave has amplitude 2, period $2\pi$, shifted right by $\frac{2\pi}{3}$, and shifted down by 3. This fully describes the graph of $$y=2\sin\left(x-\frac{2\pi}{3}\right)-3$$.