Since \( \sin\left(\frac{x}{2}\right) \) and \( \cos\left(\frac{x}{2}\right) \) oscillate between -1 and 1 within the given interval, it's challenging to pinpoint where \( f(x) \) is strictly increasing or decreasing.

However, we can observe that \( f(x) = \sin^2\left(\frac{x}{2}\right) \) is always positive within the interval. This suggests that \( f(x) \) increases as \( x \) increases, except possibly at points where \( f'(x) = 0 \) or where there are discontinuities.

Therefore, the function \( f(x) = \sin^2\left(\frac{x}{2}\right) \) is increasing on the region \([-6.18, 0.57]\).



is increasing in the region [-6.18,0.57]