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Math Help - limit for angle

  1. #1
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    limit for angle

    State the limits for B if given that B is an obtuse angle and
    a) tan2B is negative
    b) tan4B is positive
    c) tan2B is negative or tan 4B is positive
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  2. #2
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    Re: limit for angle

    Quote Originally Posted by Trefoil2727 View Post
    State the limits for B if given that B is an obtuse angle and
    a) tan2B is negative
    b) tan4B is positive
    c) tan2B is negative or tan 4B is positive
    @Trefoil2727, Why do you keep posting a list of question, but show no effort?

    From the given we know \frac{\pi}{2}<B<\pi. So any answer must be a subset of that.

    a) if \tan(2B)<0 then it must be that \frac{3\pi}{2}<2B<2\pi

    Now you do some work and show us.
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    Re: limit for angle

    Quote Originally Posted by Plato View Post
    @Trefoil2727, Why do you keep posting a list of question, but show no effort?

    From the given we know \frac{\pi}{2}<B<\pi. So any answer must be a subset of that.

    a) if \tan(2B)<0 then it must be that \frac{3\pi}{2}<2B<2\pi

    Now you do some work and show us.
    b) tan4B >0, 270<4B<450 , 540<4B<630
    67.5<B<112.5 , 135<B<157.5 ?

    I really can't understand, sorry..
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    Re: limit for angle

    hah is that means that 360<4B<720?
    so tan4B>0, 360<4B<(90+360), (180+360)<4B<(270+360)
    90<B<112.5 , 135<4B<157.5 ?

    tan2B is negative or tan 4B is positive means what?
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    Re: limit for angle

    Quote Originally Posted by Trefoil2727 View Post
    b) tan4B >0, 270<4B<450 , 540<4B<630
    67.5<B<112.5 , 135<B<157.5 ?
    I really can't understand, sorry..
    It is clear to me that you don't understand much of this, do you?

    From the given it must be true that 90^o<B<180^o. Thus any answer you find must be in that range.

    If \tan(2B)<0 then 270^o<2B<360^o or 135^o<B<180^o, which is in that range.

    If \tan(4B)>0 then it could be 180^o<4B<270^o or 45^o<B<67.5^o, which is NOT in that range.

    So we must take another course.

    Suppose that 4B\in\text{quad } I or 360^o<4B<450^o then \tan(4B)>0.
    Solving we get 90^o<B<112.5^o, which is in the range.
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