Question

The function \( y = \sin x \) is increasing in \( \left[ 0, \frac{\pi}{2} \right] \).

Hint:

The sine function is increasing in the interval \( \left[ 0, \frac{\pi}{2} \right] \) because its derivative, \( \cos x \), is positive in this range.

Answer 1

Step 1: Analyzing the function.
The function \( y = \sin x \) is a trigonometric function. We know that the sine function increases from 0 to 1 as \( x \) moves from \( 0 \) to \( \frac{\pi}{2} \). Step 2: Derivative of \( \sin x \).
The derivative of \( y = \sin x \) is \( \frac{dy}{dx} = \cos x \), which is positive for \( x \in \left[ 0, \frac{\pi}{2} \right] \). This confirms that the function is increasing in this interval. Conclusion:
Thus, the statement is True.