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trig

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sin [sin -1 (7/25) - cos -1 (-8/17)]

  • trig -

    let A = sin^-1 (7/25)
    then cosA = 24/25 ---> sinA = 7/25

    let B = cos^-1 (-8/17)
    cosB = --8/17 , let's assume B is in II
    sin B = 15/17

    so sin [sin -1 (7/25) - cos -1 (-8/17)]
    = sin (A - B)
    = sinAcosB - cosAsinB
    = (7/25)(-8/17) - (24/25)(15/17)
    = (-56 - 360)/425
    = -416/425

    check with calculator:
    A = 16.26°
    B = 118.07°
    A-B = -101.81°
    sin(-101.81°) = -.9788
    -416/425 = -.9788 , how about that?

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