Step 1 :The question is asking for the angle $s$ in the interval $[0, \frac{\pi}{2}]$ such that $\cos s = 0.6096$.
Step 2 :We can find this by using the inverse cosine function, also known as arccos. The arccos function gives the angle whose cosine is a given number.
Step 3 :However, the arccos function returns the angle in radians, so we need to convert it to degrees. We can do this by multiplying the result by $\frac{180}{\pi}$.
Step 4 :After getting the result in degrees, we need to convert it back to radians to match the question's requirement. We can do this by multiplying the result by $\frac{\pi}{180}$.
Step 5 :Doing these calculations, we find that $s = 0.9152$ radians.
Step 6 :Final Answer: The value of $s$ in the interval $[0, \frac{\pi}{2}]$ that satisfies the given statement $\cos s=0.6096$ is $s=\boxed{0.9152}$ radians.