Determine the value of the given trigonometric expression: 9. $\cos \frac{13 \pi}{12}$

Step 1 ：We are given the trigonometric expression \(\cos \frac{13 \pi}{12}\). This is not a standard angle, so we cannot directly find its cosine value.

Step 2 ：We can express \(\frac{13 \pi}{12}\) as the sum of two standard angles. We can write it as \(\frac{4 \pi}{12} + \frac{9 \pi}{12}\), which simplifies to \(\frac{\pi}{3} + \frac{3\pi}{4}\).

Step 3 ：We can use the cosine difference identity to find the cosine value. The cosine difference identity is \(\cos(a - b) = \cos a \cos b + \sin a \sin b\).

Step 4 ：Let's calculate the cosine value. Let a = 1.0471975511965976 and b = 2.356194490192345. The cosine value is approximately 0.2588190451025208.

Step 5 ：The cosine value of \(\frac{13 \pi}{12}\) is approximately 0.259.

Step 6 ：Final Answer: \(\boxed{0.259}\)