Posted by HELP!!!! on Tuesday, April 2, 2013 at 5:35am.
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.

Math  Reiny, Tuesday, April 2, 2013 at 8:40am
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
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