The set of values of ${\sec ^{ - 1}}\frac{1}{2}$ is

Since, domain of ${\sec ^{ - 1}}x$ is $R - ( - 1,1)$.

$\Rightarrow$ $( - \infty , - 1] \cup [1,\infty )$
So, there is no set of values exist for ${\sec ^{ - 1}}\frac{1}{2}$.

So, $\phi$ is the answer.