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How to calculate arctan(0) ?

  1. Apr 12, 2005 #1
    What is arctan(0)?!?!?!

    I tired using my calculator (its a ti-83 plus) I hit [sec] button then [tan] then [ 0 ] and [ ) ] and it gives me 0 as answer It is in rad mode too (deg mode is same results)

    I tried using the google calculator and it gives me 0 also!
    http://www.google.com/search?hl=en&q=arctan(0)

    BUT my math book says its pie!!!!


    Then it tried tan(pi) and indeed that does = 0!!!

    WHY!??!!? doenst arctan(0) = pi?



    Another question
    What is arctan(1/0) ??? doens that = impossible?? (if i use my calc it says cant divide by 0)

    However the answer is pi/2?!??! WHYYY


    Thanks for the help
     
    Last edited: Apr 12, 2005
  2. jcsd
  3. Apr 12, 2005 #2
    Arctan(x) = Pi means x = tan(pi)

    [tex] tan(\pi) = \frac{0up}{1left} = 0 [/tex]

    Arctan(x) = 0 means x = tan(0)

    [tex] tan(0) = \frac{0up}{1right} = 0 [/tex]

    Get it?

    2. The answer is in limits.

    [tex] arctan(1/0) = undefined [/tex]

    However the limit is defined:

    [tex] \lim x\rightarrow 0 \mbox{ of } arctan(1/x) = \frac{\pi}{2} [/tex]

    Try graphing the function arctan(x) and use the trace tool to see the values at those points.
     
  4. Apr 12, 2005 #3
    Try translating [itex] tan(x) = \frac{sinx}{cosx} [/itex], you might see it more clearly.
     
  5. Apr 12, 2005 #4

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    tan (2pi) = 0 too. So why doesn't arctan(0) = 2pi?

    Because there's an important part of the definition of arctan that you're forgetting -- go look at it again.
     
  6. Apr 12, 2005 #5

    dextercioby

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    HINT:arctan is a function.

    Daniel.
     
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