Inverse trigonometric functions reverse the standard trig functions by restricting their domains to ensure one-to-one correspondence. Since sin(x) is many-to-one on R, we restrict it to [-pi/2, pi/2] where it is bijective, and define sin^(-1): [-1, 1] -> [-pi/2, pi/2]. Similarly, cos^(-1): [-1, 1] -> [0, pi] and tan^(-1): R -> (-pi/2, pi/2). These restricted ranges are called principal value branches. The choice of branch is standardized: sin^(-1) and tan^(-1) are symmetric about the origin (centered at 0), while cos^(-1) and cot^(-1) use [0, pi] (non-negative outputs). Every answer involving inverse trig functions must lie within the principal value branch — this is the single most important rule.