Answer :

Answer:

To evaluate the expression \(\arcsin\left(\frac{1}{2}\right)\), follow these steps:

1. **Understand the Function:**

- \(\arcsin(x)\) is the inverse function of \(\sin(x)\).

- This means \(\arcsin(x)\) returns the angle \(\theta\) such that \(\sin(\theta) = x\).

2. **Identify the Range:**

- The range of \(\arcsin(x)\) is \([- \frac{\pi}{2}, \frac{\pi}{2}]\). This is the interval in which \(\theta\) will lie.

3. **Solve for the Angle:**

- We need to find the angle \(\theta\) such that \(\sin(\theta) = \frac{1}{2}\).

- Recall the unit circle or trigonometric values: \(\sin(\frac{\pi}{6}) = \frac{1}{2}\).

4. **Verify the Angle Lies in the Range:**

- \(\frac{\pi}{6}\) is within the range \([- \frac{\pi}{2}, \frac{\pi}{2}]\).

5. **Conclusion:**

- Therefore, \(\arcsin\left(\frac{1}{2}\right) = \frac{\pi}{6}\).

So, the value of \(\arcsin\left(\frac{1}{2}\right)\) is \(\frac{\pi}{6}\).