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 $\boxed{{\displaystyle \frac{1}{2}}}$.