Find the function value using coordinates of points on the unit circle. Give an exact answer. \( \cos \frac{11 \pi}{6} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \cos \frac{11 \pi}{6}=\square \) (Simplify your answer, including any radicals. Use integers or'fractions for any numbers in theraxpression.) B. The function is undefined.

To find the function value \( \cos \frac{11 \pi}{6} \), let's consider that the angle \( \frac{11 \pi}{6} \) is located in the unit circle. This angle is equivalent to \( 360^\circ - 30^\circ = 330^\circ \), which is in the fourth quadrant. The cosine of an angle in the fourth quadrant is positive. Referring to the unit circle, the coordinates at this angle are \( (\frac{\sqrt{3}}{2}, -\frac{1}{2}) \). Therefore, we have: A. \( \cos \frac{11 \pi}{6} = \frac{\sqrt{3}}{2} \) If you're curious about unit circle angles, remember that they are often expressed in radians; \( \frac{11\pi}{6} \) is one of the commonly used angles. Next time you tackle a trigonometric problem, don’t forget that memorizing these angles can save you time and improve your accuracy! Additionally, decide to learn about additional properties of the sine and cosine functions – like their periodicity or symmetry! For example, both functions have a periodicity of \( 2\pi \), which means you can always add or subtract \( 2\pi k \) (where \( k \) is any integer) to find coterminal angles with the same cosine or sine values. This little trick can really come in handy during exams!