A unique member of a set of values a variable can take, especially when seeking to define the inverse of trigonometric functions or square roots. Both 3 and –3 are square roots of 9, but $\sqrt{9}$ is chosen to be 3, the principal value.

Similarly sin30°=sin150°=sin(−210°) = 0.5, but sin⁻¹ 0.5 = 30°. Sine is not an invertible function, but by choosing principal values a function sin^–1: [–1,1]→[–90°,90°] can be defined such that sin(sin^–1x) = x for –1 ≤ x ≤ 1.

See also argument , multifunction.