The question in the image asks for the exact value of $\sec^{-1}(2)$.

To solve this:

The secant function, $\sec(\theta)$, is the reciprocal of the cosine function, meaning: $\sec(\theta) = \frac{1}{\cos(\theta)}$

Given $\sec(\theta) = 2$, we have: $\frac{1}{\cos(\theta)} = 2$

Solving for $\cos(\theta)$, we get: $\cos(\theta) = \frac{1}{2}$

We need to find the angle $\theta$ such that $\cos(\theta) = \frac{1}{2}$. This occurs at $\theta = \frac{\pi}{3}$ radians, or 60° in degrees.

Thus, the exact value of $\sec^{-1}(2)$ is $\frac{\pi}{3}$.

Would you like more details on this process or have any questions?

Here are 5 related questions for further exploration:

1. What is the relationship between secant and cosine in trigonometry?
2. How do you find the inverse of trigonometric functions like secant and cosine?
3. Why is the cosine of $\frac{\pi}{3}$ equal to $\frac{1}{2}$?
4. What is the domain and range of the secant function?
5. How do you evaluate other inverse trigonometric functions such as $\sec^{-1}(3)$?

Tip: For trigonometric functions, always check for standard angles in radians and degrees to simplify calculations.