1.5.3—Inverse trig notation

sin⁻¹, cos⁻¹ and tan⁻¹ are functions with restricted principal ranges: typically [−π/2,π/2], [0,π] and (−π/2,π/2). They undo the trig function only on those ranges.

For an equation, use the principal value first, then generate other angles with symmetry and periodicity in the stated interval.

tan⁻¹(1)=π/4, but tan x=1 also has x=π/4+nπ; the inverse notation alone gives only the principal answer.

sin⁻¹x is not 1/sin x, and swapping sin with sin⁻¹ without checking the domain changes the problem.