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Cosine inverse and cast rule

  1. Nov 14, 2012 #1
    I am currently doing a trig question and trying to find the location of the acute angles of cosine inverse and I am just wondering if cosine inverse follow the cast rule? In other words would it be positive where cos would be positive or not?
  2. jcsd
  3. Nov 14, 2012 #2


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    hi chiuda! :smile:
    for acute angles (even for negative ones), cos is always positve :confused:

    (and cos-1 is usually defined to have its principal value, which is defined to be in [0,π), and therefore is positive anyway)
  4. Nov 14, 2012 #3
    Related acute angle sorry. If cos is neg then it must be in quadrant 3 or 4.
  5. Nov 14, 2012 #4
  6. Nov 15, 2012 #5


    Staff: Mentor

    The restricted domain for the cosine function (sometimes written as Cos) is, as tiny-tim said, [0, ## \pi##]. This is the range of the inverse cosine function (cos-1). The domain for the inverse cosine function is [-1, 1]. This function maps a number in the interval [-1, 1] to a number in the interval [0, ## \pi##]. Except for 0, all the other values are positive.
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