To determine [tex]\(\cos 23^{\circ}\)[/tex], we first need to understand that the cosine function evaluates the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle for a given angle.
Using trigonometric tables, a calculator, or appropriate mathematical methods, we can find the value of [tex]\(\cos 23^{\circ}\)[/tex].
The given value for [tex]\(\cos 23^{\circ}\)[/tex] is approximately [tex]\(0.9205048534524404\)[/tex].
Now, let's compare this value with the given options:
A. [tex]\(\frac{5}{13} \approx 0.3846\)[/tex]
B. [tex]\(\frac{5}{12} \approx 0.4167\)[/tex]
C. [tex]\(\frac{12}{13} \approx 0.9231\)[/tex]
D. [tex]\(\frac{12}{5} \approx 2.4\)[/tex]
By comparing [tex]\(0.9205048534524404\)[/tex], the value closest to it is [tex]\(\frac{12}{13} \approx 0.9231\)[/tex].
Therefore, the correct answer is [tex]\( \boxed{\frac{12}{13}} \)[/tex], which corresponds to option C.
