The sine and cosine curves intersect infinitely many times , bounding regions of equal areas . Sketch one of these regions and find its area .

Explanation

To find the area of the region bounded by the sine and cosine curves, we will follow these steps:

### Step 1: Identify Points of Intersection
The sine and cosine functions intersect where \( \sin x = \cos x \). This occurs at:
\[ \tan x = 1 \implies x = \frac{\pi}{4} + n\pi, \, n \in \mathbb{Z} \]
For our calculation, we will consider the first intersection point \( x = \frac{\pi}{4} \) and the next one at \( x = \frac{5\pi}{4} \).
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