Math

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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 -

    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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