Inverse Sine Fuction

Consider the sine function f defined by f(x) = sin(x) D_f(domain)=R (real number), R_f(range) =[-1,1]

 y = Sin^-1x  iff  x = siny  and  y belongto[-π/2, π/2]

x	-π	-π/2	0	π/2	π
y	0	-1	0	1	0

It has following properties :

(1.)  Domain of sin^-1x is [-1,1]  and its range is [-π/2, π/2].

(2.)  sin(sin^-1x) = x  , for x  belongto[-1,1]  i.e  |x| ≤ 1.

(3.)sin^-1(sin y) = y, for  y  belongto[-π/2, π/2] i.e  |y|≤ π/2.