\begin{tabular}{l} In which quadrant does the terminal side of a \( \frac{5 \pi}{4} \) radian angle in standard position lie? \\ Quadrant I \\ Quadrant II \\ \hline Quadrant IV \\ \hline\end{tabular}

To determine where the terminal side of an angle of \( \frac{5\pi}{4} \) radians lies, let's break it down! This angle can be converted to degrees by multiplying by \( \frac{180}{\pi} \), which gives \( 225^\circ \). Since this angle is greater than \( 180^\circ \) but less than \( 270^\circ \), it falls into Quadrant III, a place known for its funky coordinates where both x and y values are negative! Now, for a little extra flavor, angles are measured counterclockwise from the positive x-axis in standard position. So, whipping around the circle, \( 225^\circ \) (or \( \frac{5\pi}{4} \) radians) lands you nicely in that wonderful realm called Quadrant III, really making that angle turn heads!