If $\cos A=\frac{1}{2}$, then what is the positive value of $\sin \frac{1}{2} A$, in simplest radical form with a rational denominator?
Answer Attempt 1 out of 2

Step 1 ：We are given that \( \cos A = \frac{1}{2} \).

Step 2 ：We need to find the value of \( \sin \frac{1}{2} A \).

Step 3 ：We know that \( \sin^2 A + \cos^2 A = 1 \). So, we can find the value of \( \sin A \) from the given \( \cos A \) value.

Step 4 ：Then, we can use the half-angle formula \( \sin \frac{1}{2} A = \sqrt{\frac{1-\cos A}{2}} \) to find the value of \( \sin \frac{1}{2} A \).

Step 5 ：Calculating the value of \( \sin \frac{1}{2} A \), we get 0.5.

Step 6 ：However, the question asks for the answer in simplest radical form with a rational denominator. We need to convert this decimal into a radical form.

Step 7 ：Converting 0.5 into a fraction, we get \( \frac{1}{2} \).

Step 8 ：Final Answer: The positive value of \( \sin \frac{1}{2} A \) in simplest radical form with a rational denominator is \( \boxed{\frac{1}{2}} \).