Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \tan \pi \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \tan \pi=\square \) B. \( \tan \pi \) is undefined.

A. \( \tan \pi = 0 \) Let's break it down a bit! The angle \( \pi \) radians corresponds to 180 degrees, located on the negative x-axis in the unit circle. At this position, the sine value is 0 (y-coordinate), and the cosine value is -1 (x-coordinate). Since \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), it becomes \( \tan \pi = \frac{0}{-1} = 0 \). So, it's as straightforward as that – the tangent of \( \pi \) is definitely equal to 0! Next stop – let's clarify why this isn't one of those tricky undefined situations. While some angles do pose problems for the tangent function, \( \pi \) is super clean and cuts right through with a value of 0! So bask in that mathematical glory!