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单词 inverse trigonometric function
释义
inverse trigonometric function

Mathematics
  • Sine is not a one-to-one function, and so not invertible, but ‘inverse sine’ can be defined by choosing a set of principal values. Thus, if y = sin−1 x, then x = sin y, but the converse need not hold. For each x in the interval [−1,1] there is a unique y in the interval [−π‎/2, π‎/2] such that x = sin y and this value of y is defined as y = sin−1 x.

    Similarly, for real x, y = tan−1 x if x = tan y, and the unique value y is taken from the interval (−π‎/2, π‎/2). Also, for x in the interval [−1,1], y = cos−1 x if x = cos y and the unique value y is taken from the interval [0, π‎].

    The notation arcsin, arctan, and arccos for sin−1, tan−1, and cos−1 is also used. Their derivatives are:

    inverse trigonometric function

    Graph of inverse sine

    ddx(sin1x)=11x2(x±1),ddx(cos1x)=11x2(x±1),ddx(tan1x)=11+x2.

    inverse trigonometric function

    Graph of inverse tangent

    inverse trigonometric function

    Graph of inverse cosine


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