Corresponding to each such interval, we get a branch of the
function sin–1 The branch with range 
2,
2
−π π




  is called the principal value branch,
whereas other intervals as range give different branches of sin–1 When we refer
to the function sin–1, we take it as the function whose domain is [–1, 1] and range is
2,
2
−π π




 We write  sin–1 : [–1, 1] → 
2,
2
−π π





From the definition of the inverse functions, it follows that sin (sin–1 x) = x
if  – 1 ≤ x ≤ 1 and sin–1 (sin x) = x if 
2
2
x
π
π
−
≤
≤