The graph you've provided shows a sinusoidal wave. To determine the equation of the wave, we need to analyze key aspects of the graph, such as:

1. Amplitude: The vertical distance from the midline to a peak or trough. The graph reaches a maximum of $-1$ and a minimum of $-3$, so the amplitude is half the distance between $-1$ and $-3$, which is $1$.

2. Vertical Shift: The midline of the wave is located at $y = -2$ (midway between $-1$ and $-3$).

3. Period: The horizontal length for one complete cycle of the wave. The wave completes one full cycle from $0$ to $2\pi$, so the period is $2\pi$.

4. Phase Shift: The graph starts at $x = 0$ and appears to follow a cosine-like wave, though reflected vertically.

Based on these observations, we can write the equation of the sinusoidal wave as:

$y = -\cos(x) - 2$

Where:

• The negative sign reflects the wave vertically.
• The $\cos(x)$ suggests it follows a cosine function.
• The $-2$ represents the vertical shift.

Let me know if you'd like more details or clarifications on this.

Related Questions:

1. What is the general form of a sinusoidal function?
2. How do you determine the phase shift of a trigonometric graph?
3. What does the period of a wave tell you in trigonometric functions?
4. How does changing the amplitude affect the graph of a trigonometric function?
5. What is the difference between sine and cosine waves?

Tip: To graph any trigonometric function, it's important to first identify the amplitude, period, phase shift, and vertical shift.