value of sin inverse sin x between -5pie by 2 to -3 pie by 2

Dear Student,

The value of sin^(-1)sin (x) = x only if x lies between [-pi/2, pi/2]

But in your problem, x lies between [-5pi/2, -3pi/2] and thus we need to use reductin formula to bring this interval in the desired range. and thus we found that,

sin^(-1)sin(x) = 2pi + x, ifx lies between [-5pi/2, -3pi/2].

Best of luck!