1. The problem is to solve the equation $\frac{1}{2}\sin(2a) = 4$ for $a$. 2. Start by isolating $\sin(2a)$: multiply both sides by 2 to get $$\sin(2a) = 8$$ 3. Recall that the sine function has a range of $[-1,1]$, meaning $\sin(2a)$ cannot be greater than 1 or less than -1. 4. Since 8 is outside the range of sine, there is no real solution to this equation. 5. Therefore, the equation $\frac{1}{2}\sin(2a) = 4$ has no real solutions.