The inverse trig functions have distinct parity behaviors. Odd functions (symmetric about origin): sin^(-1)(-x) = -sin^(-1)(x), tan^(-1)(-x) = -tan^(-1)(x), csc^(-1)(-x) = -csc^(-1)(x). Pi-complement functions: cos^(-1)(-x) = pi - cos^(-1)(x), cot^(-1)(-x) = pi - cot^(-1)(x), sec^(-1)(-x) = pi - sec^(-1)(x). The difference arises from the range: functions with ranges symmetric about 0 (like [-pi/2, pi/2]) are odd, while those with ranges [0, pi] undergo the pi-complement transformation. These properties are essential for simplifying expressions with negative arguments.