Find the indicated function value. If it is undefined, say so. \[ \begin{array}{l}\text { cot } 270^{\circ}\end{array} \] \( \begin{array}{r}\text { A. cotect the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. } 16.24 \text { of } 1.3 .65\end{array} \) B. The function is undefined.

The cotangent function, cot, is defined as the ratio of the adjacent side to the opposite side in a right triangle or, in terms of sine and cosine, as \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \). At \( 270^{\circ} \), the sine value is \( -1 \) and the cosine value is \( 0 \). Since you can't divide by zero, the cotangent at this angle results in an undefined value. Thus, the cotangent of \( 270^{\circ} \) is undefined, which confirms option B. When working with trigonometric functions, it's vital to remember the unit circle. At every quadrant, the functions have specific values. In the third quadrant, both sine and cosine return negative values; however, some functions can become undefined where the sine function equals zero—like at \( 0^{\circ} \), \( 180^{\circ} \), and \( 360^{\circ} \). Remembering those landmarks can help prevent such confusion!