The set of values of `sec^(-1)(1/2)` is `"……….."`

Explanation

To find the set of values of \( \sec^{-1}\left(\frac{1}{2}\right) \), we will follow these steps:

### Step 1: Understand the function
The function \( \sec^{-1}(x) \) is the inverse of the secant function. The secant function, \( \sec(\theta) \), is defined as:
\[ \sec(\theta) = \frac{1}{\cos(\theta)} \]
The range of \( \sec^{-1}(x) \) is defined for \( x \leq -1 \) or \( x \geq 1 \).

### Step 2: Check the value \( \frac{1}{2} \)
We need to check if \( \frac{1}{2} \) falls within the valid range of the secant function. Since \( \frac{1}{2} \) is between -1 and 1, it does not fall within the acceptable range for the secant function.

### Step 3: Conclusion
Since \( \frac{1}{2} \) is not in the range of \( \sec(\theta) \), it implies that there is no angle \( \theta \) such that \( \sec(\theta) = \frac{1}{2} \). Therefore, the set of values of \( \sec^{-1}\left(\frac{1}{2}\right) \) is empty.

### Final Answer
The set of values of \( \sec^{-1}\left(\frac{1}{2}\right) \) is:
\[ \emptyset \quad \text{(null set)} \]

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