Question: User: P = 1/\pi \cos^{-1}(25.8 / \sqrt{26.8 \times 25.2})
1. **State the problem:** We need to evaluate the expression $$P = \frac{1}{\pi} \cos^{-1}\left(\frac{25.8}{\sqrt{26.8 \times 25.2}}\right)$$.
2. **Recall the formula and rules:** The inverse cosine function, \(\cos^{-1}(x)\), returns an angle whose cosine is \(x\). The expression involves division and a square root inside the argument of \(\cos^{-1}\).
3. **Calculate the denominator inside the square root:**
$$\sqrt{26.8 \times 25.2} = \sqrt{675.36}$$
4. **Evaluate the square root:**
$$\sqrt{675.36} = 25.98$$
5. **Calculate the fraction inside the inverse cosine:**
$$\frac{25.8}{25.98}$$
6. **Simplify the fraction:**
$$\frac{25.8}{25.98} = \frac{\cancel{25.8}}{\cancel{25.98}} \approx 0.993$$
7. **Evaluate the inverse cosine:**
$$\cos^{-1}(0.993) \approx 0.116 \text{ radians}$$
8. **Divide by \(\pi\):**
$$P = \frac{0.116}{\pi} \approx 0.037$$
**Final answer:**
$$P \approx 0.037$$