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The problem provided asks to determine the equation of the graph, which is of the form \( y = a \sin(bx) \) or \( y = a \cos(bx) \), where \( b > 0 \).

### Let's break it down based on the graph:

1. **Amplitude (a):**
   - The maximum value of the graph is 2, and the minimum value is -2. This suggests that the amplitude \( a \) is 2. 
   
2. **Period:**
   - The graph completes one full cycle from \( x = 0 \) to \( x = \frac{2\pi}{3} \), which means the period \( T \) is \( \frac{2\pi}{3} \).
   - The period of a sinusoidal function is given by \( T = \frac{2\pi}{b} \), so we can set this equal to \( \frac{2\pi}{3} \) and solve for \( b \):
     \[
     \frac{2\pi}{b} = \frac{2\pi}{3} \implies b = 3
     \]

3. **Sine or Cosine:**
   - At \( x = 0 \), the graph is at its maximum value (2), which is characteristic of a cosine graph. A sine graph typically starts at 0. Hence, the function is of the form \( y = a \cos(bx) \).

### Putting it all together:
The equation of the graph is:
\[
y = 2 \cos(3x)
\]

Would you like any more details, or do you have any questions?

### Relative Questions:
1. How do we determine the amplitude of a trigonometric graph?
2. What is the difference between the sine and cosine graphs in terms of their starting points?
3. How do you find the period of a trigonometric function from the graph?
4. What role does the value of \( b \) play in a trigonometric equation?
5. How can you recognize a phase shift in a trigonometric graph?

**Tip:** The amplitude affects the vertical stretch of the graph, while the period affects its horizontal compression/stretch.

The function graphed is of the form y = a sin(bx) or y = a cos(bx), where b > 0. Determine the equation of the graph.

Solve a trigonometric graphing problem where you determine the equation of a cosine function. The amplitude is 2, and the period is 2π/3. Learn how to calculate amplitude, period, and determine whether the graph represents a sine or cosine function.

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