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    Hi!

    I came across this question in my book and as you can see in the first attached pic I was only able to find one half-line (pi/3).

    According to the book there are two half-lines (pic 2).

    Can anyone tell me where the second one (-2pi/3) comes from?

    Any help would be greatly appreciated
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    (Original post by WatermelonJuice1)
    Hi!

    I came across this question in my book and as you can see in the first attached pic I was only able to find one half-line (pi/3).

    According to the book there are two half-lines (pic 2).

    Can anyone tell me where the second one (-2pi/3) comes from?

    Any help would be greatly appreciated
    tanθ = √ 3

    has solutions in a full circle
    θ = π/3
    θ =4 π/3 = -2 π/3

    does this help?
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    (Original post by TeeEm)
    tanθ = √ 3

    has solutions in a full circle
    θ = π/3
    θ =4 π/3 = -2 π/3

    does this help?
    It did help, but in the previous question they only wanted the half-line given by the first result which confused me.
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    (Original post by WatermelonJuice1)
    It did help, but in the previous question they only wanted the half-line given by the first result which confused me.
    I know nothing about the previous question
    questions are different.
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    (Original post by TeeEm)
    I know nothing about the previous question
    questions are different.
    The previous Q (part a of the same question) was the following:

    arg(z)=arctan(2)

    arctan(2)=63.4 , 243.4

    Both can be represented on an Argand diagram but in the back of the book, only the first one is.

    Am I always expected to find both? Would this be specified in an exam? Thanks.
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    (Original post by WatermelonJuice1)
    The previous Q (part a of the same question) was the following:

    arg(z)=arctan(2)

    arctan(2)=63.4 , 243.4

    Both can be represented on an Argand diagram but in the back of the book, only the first one is.

    Am I always expected to find both? Would this be specified in an exam? Thanks.
    the arctan2 = 63.4 and NOT 243.4

    the statement tanθ = 2 and arctan2 = θ are NOT equivalent as the tan is NOT a one to one function

    a simple analogy

    x2=4 and x = √4 are not euivalnent
    the first has 2 answers the second has 1 answer
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    (Original post by TeeEm)
    the arctan2 = 63.4 and NOT 243.4

    the statement tanθ = 2 and arctan2 = θ are NOT equivalent as the tan is NOT a one to one function

    a simple analogy

    x2=4 and x = √4 are not euivalnent
    the first has 2 answers the second has 1 answer
    Ok, I get it now. Thanks a lot.
 
 
 
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