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The graph shown is a sine function of the form \( f(x) = \sin(x + p) \). The goal is to determine the value of the phase shift \( p \).

### Analyzing the Graph:

1. **Key Observation**: The graph of \( f(x) = \sin(x + p) \) has been shifted horizontally by a phase shift \( p \).
2. **Maximum Point**: The maximum of the sine function typically occurs at \( x = 90^\circ \) for \( \sin(x) \), but in the graph, the maximum point occurs at \( x = 0^\circ \). 

### Calculating \( p \):

- Since the maximum point has shifted from \( 90^\circ \) to \( 0^\circ \), the phase shift \( p \) must satisfy:
  \[
  90^\circ + p = 0^\circ
  \]
- Solving for \( p \):
  \[
  p = -90^\circ
  \]

Thus, the value of \( p \) is \( -90^\circ \).

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What happens to the graph of \( \sin(x) \) if \( p \) is positive?
2. How does a vertical shift affect the graph of \( \sin(x) \)?
3. How would the graph change if the amplitude were altered?
4. What is the general form of a sinusoidal function with both phase shift and vertical shift?
5. How do you determine the period of a sine function with a modified coefficient?

**Tip:** Understanding phase shifts is crucial for graphing trigonometric functions. Remember, a positive phase shift moves the graph to the left, while a negative phase shift moves it to the right.

Calculate the value of p for the function f(x) = sin(x + p) given the graph, where the maximum point of the graph occurs at x = 0 degrees.

Learn how to calculate the phase shift (p) in the sine function f(x) = sin(x + p) using a given graph. Understand the horizontal shift and determine the phase shift based on the maximum point of the sine curve. Suitable for high school students in Grades 10-12.

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