Question

If y = sin−1 x, then sin y = x,−π/2 ≤ y ≤ π/2.

Therefore, to find
y = sin−1(−3/22, we must find an angle y whose sine is -3/2.

There are many possible angles with this sine, but the range of
y = sin−1 x
is restricted to [ , ] and so y must be in this interval.

Answer 1

I will assume you have a typo and you meant to say
" we must find an angle y whose sine is -3/22 "
since sin y = -3/2 is not possible.

I see this question summarized to ...

find Ø if sin Ø = -3/22 , -π/2 ≤ Ø ≤ π/2
so Ø is in III or IV
but within the restriction given, Ø can only be in IV

set your calculator to radians and find
A if sinA = +3/22
A = .1368

then Ø = 0 - .1368 = -.1368

using your notation:
y = -.1368


check:
sin^-1 (-.1368) = -.13637
and -3/22 = -.13636 , not bad