State for any acute angle `theta` whether :
`sintheta` increases or decreases as `theta` increases.

Answer

To determine whether \(\sin \theta\) increases or decreases as \(\theta\) increases for any acute angle \(\theta\), we can analyze the values of \(\sin \theta\) at various standard angles and also consider the geometric interpretation of sine in a right triangle.

### Step 1: Understanding the Values of Sine at Standard Angles
We can look at the sine values for standard angles in the range of \(0^\circ\) to \(90^\circ\):
- \(\sin 0^\circ = 0\)
- \(\sin 30^\circ = \frac{1}{2} = 0.5\)
- \(\sin 45^\circ = \frac{1}{\sqrt{2}} \approx 0.707\)
- \(\sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866\)
- \(\sin 90^\circ = 1\)

### Step 2: Observing the Trend
From the values listed above, we can observe that as \(\theta\) increases from \(0^\circ\) to \(90^\circ\):
- \(\sin 0^\circ < \sin 30^\circ < \sin 45^\circ < \sin 60^\circ < \sin 90^\circ\)

This indicates that the sine values are increasing as \(\theta\) increases.

### Step 3: Geometric Interpretation
In a right triangle, the sine of an angle \(\theta\) is defined as the ratio of the length of the opposite side (perpendicular) to the length of the hypotenuse. As \(\theta\) increases:
- The length of the opposite side increases relative to the hypotenuse.
- Thus, the value of \(\sin \theta\) (which is the ratio of the opposite side to the hypotenuse) also increases.

### Conclusion
From both the numerical values and the geometric interpretation, we can conclude that for any acute angle \(\theta\), \(\sin \theta\) increases as \(\theta\) increases.