The problem is asking to find the value of $s$ in the interval $\left[0, \frac{\pi}{2}\right]$ such that:

$\tan(s) = 0.7998$

To solve for $s$, you will take the inverse tangent (or arctangent) of 0.7998, which will give you the value of $s$ in radians. Here's the process:

$s = \tan^{-1}(0.7998)$

Let me calculate that for you.The value of $s$ that satisfies $\tan(s) = 0.7998$ in the interval $\left[0, \frac{\pi}{2}\right]$ is approximately $s = 0.6746$ radians, rounded to four decimal places.

Would you like any further details or explanations?

Here are some related questions for practice:

1. What is the derivative of the tangent function?
2. How would you solve for $s$ if the interval was $[0, 2\pi]$?
3. What is the value of $\tan(s)$ when $s = \frac{\pi}{4}$?
4. How would you convert this angle $s$ from radians to degrees?
5. What is the general solution for $\tan(s) = 0.7998$ on the real line?

Tip: When dealing with trigonometric functions, be mindful of the given interval as it affects the uniqueness of the solution.