\( \begin{array}{llll}\text { (c) } \sec \left(\frac{23 \pi}{12}\right) & \text { (f) } \csc \left(\frac{7 \pi}{4}\right) & \text { (g) } \cot \left(\frac{3 \pi}{4}\right) & \text { (h) } \sin \left(\frac{19 \pi}{12}\right) \\ \text { (i) } \tan \left(-\frac{11 \pi}{6}\right) & \text { (j) } \cot \left(\frac{13 \pi}{2}\right) & \text { (k) } \csc \left(-\frac{7 \pi}{4}\right) & \text { (l) } \cot (225)\end{array} \)

Did you know that angles can extend beyond the basic \(0\) to \(2\pi\) range? For instance, \(\frac{23\pi}{12}\) is equivalent to a larger angle that can be worked into the standard unit circle framework by subtracting \(2\pi\) (or \(12\pi/12\)). So, \(\sec\left(\frac{23\pi}{12}\right)\) actually falls into the fourth quadrant, where the secant function is negative. When evaluating trigonometric functions like \(\csc\left(-\frac{7\pi}{4}\right)\), keep in mind that the cosecant is the reciprocal of the sine. The angle \(-\frac{7\pi}{4}\) is equivalent to \(\frac{\pi}{4}\) in the positive direction (as it wraps around the unit circle), which means \(\csc\left(-\frac{7\pi}{4}\right) = \csc\left(\frac{\pi}{4}\right) = \frac{1}{\sin\left(\frac{\pi}{4}\right)} = \sqrt{2}\).