Increasing or Decreasing Analysis of f(x) = sinx in interval (0, π/2)

Sin(x) is a trigonometric function that oscillates between -1 and 1 as x increases from 0 to π/2. To determine if f(x) = sinx is increasing or decreasing in this interval, we need to analyze its derivative.

Determination of Derivative
The derivative of f(x) = sinx is f'(x) = cosx. In the interval (0, π/2), the cosine function is always positive since it represents the x-coordinate of points on the unit circle in the first quadrant.

Analysis of f'(x) = cosx
Since cosx is positive in the interval (0, π/2), the derivative f'(x) = cosx is positive. This means that the function f(x) = sinx is increasing in this interval.

Conclusion
In the interval (0, π/2), the function f(x) = sinx is increasing as x increases. This can be explained by the fact that the cosine function, which is the derivative of sinx, is positive in this interval. Therefore, as x moves from 0 to π/2, the values of sinx also increase, making the function f(x) = sinx an increasing function in this interval.