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Working out angles without calculator (complex numbers)

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    Hi guys,

    If I have a triangle, of which I know all the sides (I'm working with complex numbers) im trying to work out the ARGUMENT i.e arctan (y/x) without a calculator.
    This is just the angle between my hypotenuse which is 2 root 2 and my adjacent which =2. Opposite is also 2.

    How can I do this?

    Thanks, really stuck.
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    If you're looking for angles, you want to start with the cosine rule. Square all the sides and look at what that tells you.
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    That's half a right angle.
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    Sounds like you're dealing with a right-angled isosceles triangle (i.e. half a square) - since the opposite and adjacent are both 2, and the triangle obeys Pythagoras' theorem.
    Should be obvious what the angle is...
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    Isn't the answer: arg= tan-1 1= (pi)/4 = 45o
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    Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

    Thanks
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    (Original post by dannylfc_1)
    Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

    Thanks
    It's been suggested...the cosine rule. In general for a triangle with integral sides the angles will not be rational
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    (Original post by dannylfc_1)
    Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3.
    These is no general method that will work for everything.

    You should know (*) the values of \sin \theta, \cos \theta for any integer multiple of \pi / 6 or \pi / 4.

    All the examples you have given fall into this category, and this is likely no coincidence.

    (*) Or be able to work out from a value you do know. e.g. I might not know directly what sin(3pi/4) is, but I know that sin(3pi/4) = sin(pi - 3pi/4) = sin(pi/4) = sqrt(2)/2.
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    (Original post by dannylfc_1)
    Yes ok, I gave a simple example, but I want a general method that I can use for everything. For example, the next question has hypotenuse = 2, adjacent = 1, and opposite = root 3

    Thanks
    okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?
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    (Original post by pauching)
    okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?
    yes sorry - the angle between adjacent and hypotenuse.
    I see the cosine rule has been mentioned but can someone spell this out for me exactly how you work it out. Maths isn't my strongest subject!
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    (Original post by DFranklin)
    These is no general method that will work for everything.

    You should know (*) the values of \sin \theta, \cos \theta for any integer multiple of \pi / 6 or \pi / 4.

    All the examples you have given fall into this category, and this is likely no coincidence.

    (*) Or be able to work out from a value you do know. e.g. I might not know directly what sin(3pi/4) is, but I know that sin(3pi/4) = sin(pi - 3pi/4) = sin(pi/4) = sqrt(2)/2.
    Yes, I understand, so how then do I work out arctan? Thanks
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    If you know the values for sin and cos, you know the value for tan...
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    (Original post by dannylfc_1)
    yes sorry - the angle between adjacent and hypotenuse.
    I see the cosine rule has been mentioned but can someone spell this out for me exactly how you work it out. Maths isn't my strongest subject!
    In a triangle where the side of length a is opposite angle A, a^2=b^2+c^2-2bc cos A
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    (Original post by pauching)
    okay, but you didn't tell which angle you want to find (ie. angle between hyp and opp or angle between hyp and adj). Yea I also think that you should you cosine rule. Anyway, I don't see what both your questions have to do with complex number...?
    I also should have said minus root 3 not root 3

    Its because my complex number is z=1-i root 3 and i want to put this in the form re^i(theta). Where r is the hypotenuse which is 2 and theta is the angle arctan. Hope that helps
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    A squared = B squared + C squared - (2BC) x Cos A

    just rearrange the formula to make cos A the subject of the equation and you can work out each one
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    Yes thanks, i understand the cosine rule method. Thanks everyone for helping really appreciated
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    Have to say, I strongly disagree with everyone advocating the use of the cosine formula.
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    (Original post by DFranklin)
    Have to say, I strongly disagree with everyone advocating the use of the cosine formula.
    How else would you do it? I realise I'm getting to the point where I have cos A = x. But then I still need to know how to do the next part in my head, to which I think i might just have to memorise the unit circle.
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    If you have a right angled triangle, you don't need the cosine formula. This is basic (GCSE, I would have thought) trig.
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Updated: March 23, 2012
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