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Math Help - Arctangents in a half-open interval?

  1. #1
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    Arctangents in a half-open interval?

    The equation is tan^2(X) = 2tan(X) where X is an element of [0, 360)

    As you can see, the interval is half-open. My question is, will the solution look like this:

    X = arctan A = tan^-1(A) + 180n because inverse tangents come in pairs a half revolution apart

    or this:

    X = arctan A = tan^-1(A) + 90n because the system is only half open?



    (X=Theta but I don't know how to make the symbol)
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  2. #2
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    Quote Originally Posted by lauriestar View Post
    The equation is tan^2(X) = 2tan(X) where X is an element of [0, 360)

    As you can see, the interval is half-open. My question is, will the solution look like this:

    X = arctan A = tan^-1(A) + 180n because inverse tangents come in pairs a half revolution apart

    or this:

    X = arctan A = tan^-1(A) + 90n because the system is only half open?
    the interval 0 \leq x < 360 just excludes a single value, 360 degrees, nothing more.


    \tan^2{x} = 2\tan{x}

    \tan^2{x} - 2\tan{x} = 0

    \tan{x}(\tan{x} - 2) = 0

    \tan{x} = 0 ... x = 0, x = 180 (note that x = 360 is excluded)

    \tan{x} = 2 ... x = \arctan(2) , x = \arctan(2) + 180
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