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Math Help - ArcTan(x,y) formula

  1. #1
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    Post ArcTan(x,y) formula

    Hi,

    I need an idiot's guide on how to calculate ArcTan(x,y), can somebody please help?

    I have a working example (below) but have no idea how it works:

    α = arctan(sin(12.0321) * cos(23.45), cos(12.0321)) = 11.0639

    Incidentally, in order to calculate sin and cos (in VB Code) I have to convert the degrees to radians first - will this mess up the output or can I just convert it back into degrees again?

    Thanks for looking,

    Chris.
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  2. #2
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    Opalg's Avatar
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    Quote Originally Posted by Chris147 View Post
    I need an idiot's guide on how to calculate ArcTan(x,y), can somebody please help?

    I have a working example (below) but have no idea how it works:

    α = ArcTan(sin(12.0321) * cos(23.45), cos(12.0321)) = 11.0639

    Incidentally, in order to calculate sin and cos (in VB Code) I have to convert the degrees to radians first - will this mess up the output or can I just convert it back into degrees again?
    This is a weird definition of ArcTan, certainly not a standard one. Normally, arctan is a function of one variable, not two, and arctan(x) basically means the angle whose tangent is x. I'll refer to this function of one variable as arctan (with lower case a and t) to distinguish it from that function ArcTan of two variables.

    If you work out sin(12.0321) * cos(23.45), it comes to 0.1912425; and cos(12.0321) is 0.9780309. So we are told that ArcTan(0.1912425,0.9780309) = 11.0639. What I found by trial and error is that if I divide 0.1912425 by 0.9780309 it comes to 0.1955383. Then when I press the \tan^{-1} button on my calculator (remember that \tan^{-1} is just another name for arctan), it gives the answer as 11.0639, which is what we want.

    So it seems to me as though your ArcTan is related to the conventional arctan by the relation ArcTan(x,y) = arctan(x/y).
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  3. #3
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    ArcTan(x/y) not (x,y)

    Hi Opalg

    First of all, thank you.

    I don't think I would have figured that out in a month of Sundays.

    All I need to do now is create a ArcTan function (of the standard ArcTan(x) variety) - unfortunately Access VBA doesn't support or list it in the derived Math Functions). This shouldn't prove too difficult though - I've already done the same ArcSin and ArcCos.

    If anyone has an outline of how ArcTan(x) is calculated I'd appreciate it, meanwhile - thanks again, your help is greatly appreciated.

    Chris.
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  4. #4
    Super Member ebaines's Avatar
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    If you already have a function that determines arcsin(x), then you can determine arctan(x) as follows:

    arctan(x) = arcsin (x/sqrt(x^2+1))

    For example: arctan(3/4) = arcsin[(3/4)/(5/4)] = arcsin(3/5)

    Another approach would be to use the sequence:

    arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...

    which converges for x<=1. If x>1, just remember that arctan(x) = pi/2-arctan(1/x).
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  5. #5
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    ArcTan Formula

    Thanks ebaines,

    that's pretty much fixed the whole thing :-).

    Thanks also to the Math Help Forum for a great service.

    Chris.
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