The eternal mathematical torment of trigonometry! When you solve sin(x) = 0.5 and proudly write x = π/6, your teacher channels their inner Bernie and demands the COMPLETE answer with that pesky +2kπ term! Why? Because in the circular world of trig functions, solutions repeat every 2π radians - they're like that song you can't get out of your head, coming back FOREVER. Your single answer is technically an infinite family of solutions, and your teacher won't rest until you acknowledge ALL your mathematical children! 🔄📐