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The image shows a graph with two curves, labeled (d) and (e). These curves are plotted against an angular scale on the x-axis, ranging from \(-30^\circ\) to \(180^\circ\). The equations provided are:

- (d) \(y = \sin(x + p)\)
- (e) \(y = \cos(x + q)\)

### Identifying the Graphs:

1. **Graph (d)**: The equation \(y = \sin(x + p)\) represents a sine wave that has been horizontally shifted by \(p\) units. This shift can be determined by observing the graph. Typically, the sine function starts at \(y = 0\) when \(x = 0\), reaches a maximum at \(90^\circ\), and returns to \(0\) at \(180^\circ\).

2. **Graph (e)**: The equation \(y = \cos(x + q)\) represents a cosine wave that has been horizontally shifted by \(q\) units. A standard cosine function starts at \(y = 1\) when \(x = 0\), drops to \(0\) at \(90^\circ\), and reaches a minimum at \(180^\circ\).

### Analyzing the Given Graphs:
- The graph labeled (d) starts at \(x = -30^\circ\) with \(y\) close to zero, reaches its peak between \(60^\circ\) and \(90^\circ\), and crosses zero again near \(150^\circ\). This behavior resembles a sine curve, confirming that (d) corresponds to \(y = \sin(x + p)\).

- The graph labeled (e) starts at a peak around \(x = 0^\circ\), falls to zero between \(60^\circ\) and \(90^\circ\), and continues downward. This corresponds to the typical behavior of a cosine curve, confirming that (e) corresponds to \(y = \cos(x + q)\).

### Horizontal Shifts:
- **For \(y = \sin(x + p)\)**: Since the sine curve seems to start just before \(x = 0^\circ\), the shift \(p\) could be negative (i.e., to the left).
  
- **For \(y = \cos(x + q)\)**: The cosine curve appears to start close to \(x = 0^\circ\), so \(q\) might be close to zero or slightly positive.

### Conclusion:
- Graph (d) is \(y = \sin(x + p)\) with a horizontal shift.
- Graph (e) is \(y = \cos(x + q)\) with a possible small horizontal shift.

Would you like more detailed explanations or have any specific questions?

### Related Questions:
1. How would the graph change if the shift \(p\) was positive instead of negative for the sine function?
2. What is the amplitude of the given sine and cosine functions?
3. How would the graph be affected if a vertical shift was introduced to \(y = \sin(x + p)\) or \(y = \cos(x + q)\)?
4. How can you determine the phase shift \(p\) or \(q\) from the graph more precisely?
5. What would the graphs look like if the equations were \(y = \sin(2x + p)\) or \(y = \cos(2x + q)\)?

### Tip:
To determine phase shifts more accurately, look for where the curve crosses the x-axis or reaches its maximum/minimum compared to the standard sine or cosine curve.

Identify the graphs and determine their corresponding equations based on the given sine and cosine functions: y = sin(x + p) and y = cos(x + q).

This problem involves identifying the graphs of sine and cosine functions with horizontal shifts. Detailed analysis of the phase shifts for y = sin(x + p) and y = cos(x + q) is provided, suitable for students in Grades 10-12.

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