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The image contains a math problem related to the graphs of two trigonometric functions:

- \( f(x) = \sin x \)
- \( g(x) = \cos x \)

The task involves determining the area of a region bounded by these two curves and certain points of intersection. Here’s a breakdown of the key steps:

### Problem Explanation:
1. **Functions:** 
   - \( f(x) = \sin x \)
   - \( g(x) = \cos x \)
   
   These are graphed on the interval \([0, 2\pi]\).

2. **Points of Interest:**
   - Points \( A \) and \( B \) are where \( f(x) \) and \( g(x) \) intersect.
   - \( C \) is a point on \( f(x) \) where line \( AB \) is divided in the ratio 1:3.
   - The shaded region \( BCD \) is part of the area we are asked to find.
   
3. **Objective:**
   - Find the area of the region \( BCD \).
   
Let me calculate and explain the steps to find the required area.

### Approach:
1. **Find points of intersection:** Solve for \( f(x) = g(x) \) to get the points \( A \) and \( B \).
2. **Determine the coordinates of point \( C \),** which divides the segment \( AB \) in a ratio of 1:3.
3. **Find point \( D \) on the graph of \( g(x) \)** such that the straight line through \( C \) and the x-axis passes through \( D \).
4. **Compute the area of the region \( BCD \)** using integration.

I'll proceed with the necessary calculations now.The area of the region bounded between the curves \( f(x) = \sin x \) and \( g(x) = \cos x \) from \( A \) (where \( x = \frac{\pi}{4} \)) to \( B \) (where \( x = \frac{5\pi}{4} \)) is approximately 2.83 square units.

This value represents the area between the curves. To find the exact area of the region \( BCD \), further steps are required based on the points \( C \) and \( D \).

Would you like to proceed with these additional calculations or clarifications?

Here are 5 questions related to this:

1. How do we calculate the coordinates of point \( C \) using the 1:3 ratio?
2. How do we find the equation of the line passing through points \( C \) and \( B \)?
3. What method can we use to determine the area of more complex regions like \( BCD \)?
4. How do we verify the symmetry between \( \sin x \) and \( \cos x \)?
5. How does changing the interval affect the total area?

**Tip:** When calculating areas between curves, always ensure the integration limits correspond to the points of intersection to get accurate results.

Determine the area of the region BCD as described by the curves y = sin(x) and y = cos(x) between [0, 2π] with specific conditions for points A, B, C, and D.

Learn how to find the area of a region bounded by trigonometric curves y = sin(x) and y = cos(x) between [0, 2π]. This problem involves understanding intersections, ratios, and integration techniques, suitable for advanced high school or first-year calculus students.

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