The given equation is:

\[
y = -\cos\left(\frac{1}{2}(x - \frac{\pi}{7})\right)
\]

This represents a transformed cosine function. Let's break down its components:

### 1. **Amplitude**: 
   - The coefficient in front of the cosine function is `-1`. This means the amplitude is \(1\), but the negative sign reflects the graph over the x-axis.
   
### 2. **Period**:
   - The period of a standard cosine function is \(2\pi\). The period of the transformed function is affected by the coefficient \(\frac{1}{2}\) inside the cosine function.
   - The formula for the period is:
     \[
     \text{Period} = \frac{2\pi}{\frac{1}{2}} = 4\pi
     \]

### 3. **Phase Shift**:
   - The phase shift is determined by \(\frac{\pi}{7}\). Since it appears as \(x - \frac{\pi}{7}\), the graph is shifted to the right by \(\frac{\pi}{7}\).

### 4. **Vertical Shift**:
   - There is no vertical shift since there is no constant added outside the cosine function.

### Summary of transformations:
   - Amplitude: 1 (with reflection over x-axis)
   - Period: \(4\pi\)
   - Phase shift: \(\frac{\pi}{7}\) to the right
   - Vertical shift: None

Would you like to see a graph of this function, or would you like to discuss it further?

### Related Questions:
1. What is the domain and range of this transformed function?
2. How does a vertical shift affect the cosine function?
3. What is the maximum and minimum value of this function?
4. How does the phase shift impact the starting point of the graph?
5. How do we compute the x-intercepts of this function?

### Tip:
For trigonometric transformations, always identify changes in amplitude, period, and phase shift first to understand the graph's behavior.

Explore how to analyze the transformed cosine function y = -cos[1/2(x - pi/7)] by examining its amplitude, period, and phase shift. This detailed explanation covers key trigonometric transformations, ideal for students in Grades 10-12.

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