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Math Help - negative exponents

  1. #1
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    Question negative exponents

    What does a negative exponent in front of number mean?
    Example: sin ^-1 (0.53)
    This is a problem involving refraction of light through two mediums such as water and air applying Snell's Law.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dwedel View Post
    What does a negative exponent in front of number mean?
    Example: sin ^-1 (0.53)
    This is a problem involving refraction of light through two mediums such as water and air applying Snell's Law.
    In general, it means an inverse (or when dealing with numbers, a reciprocal).

    In this particular example, though, \sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right). It must be emphasized that \sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r  ight)^{-1}.

    Does this help??
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    In general, it means an inverse (or when dealing with numbers, a reciprocal).

    In this particular example, though, \sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right). It must be emphasized that \sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r  ight)^{-1}.

    Does this help??
    In other words, if you had the equation \sin^{-1}(0.53) = x (say), it is asking you what angle (x) would be needed to have

    \sin{x} = 0.53 hold true.
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    In general, it means an inverse (or when dealing with numbers, a reciprocal).

    In this particular example, though, \sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right). It must be emphasized that \sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r  ight)^{-1}.

    Does this help??
    Yes it does. Thanks. dwedel
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