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
−
≤
≤ In other words, if y = sin–1 x, then
sin y = x Remarks
(i)
We know from Chapter 1, that if y = f(x) is an invertible function, then  x = f –1 (y)