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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