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Tan -1 of infinity

  1. May 1, 2009 #1
    this isn't hw just wanted to know what the values are.

    tan -1 (infinity) = pi/2
    tan-1 (0) = 0

    what is sin -1 infinty and cos -1 infinity?
  2. jcsd
  3. May 1, 2009 #2


    Staff: Mentor

    Looks like LaTeX isn't working again.

    The second one is correct, but not the first one. What you can say, though, is that
    lim(x -->infinity) tan-1(x) = pi/2

    The domain of the inverse tangent function is all real numbers, but neither -infinity nor infinity is included in that set.
    The domain for sin-1(x) is usually taken as [-pi/2, pi/2], and the domain for cos-1(x) is usually taken as [0, pi]. These intervals are chosen to make these function one-to-one, which a function has to be in order for it to have an inverse.

    Unline tan-1(x), neither the inverse sine nor inverse cosine have limits as x approaches infinity, so the answer to your last questions is that they aren't anything.
  4. May 1, 2009 #3
    o ok thanks so only tan-1 (x) as x goes to infinty is pi/2
  5. May 2, 2009 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    That is the simplest way to think of it. Using the symbol [itex]\infty[/itex] is often useful shorthand for the same thing. It can also be put on a sound rigorous footing geometrically (projective space) or analytically (Riemann sphere), but that requires using spaces strictly larger than the real (or complex) numbers.
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