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Math Help - Trigonometry

  1. #1
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    Trigonometry

    If y= arctan x and x<0 then y lies in what quadrant ?
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  2. #2
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    In the co-ordinate axis, if the angle subtended at the origin is θ, then tanθ = y/x. tanθ will be negative when x will be negative of y will be negative. Now decide in which quadrant the angle will be?
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  3. #3
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    tanθ will be negative when x will be negative of y will be negative.
    \tan\theta<0 when x < 0 and y > 0 or y < 0 and x > 0. Also, one must take into account that arctan returns angles between -\pi/2 and \pi/2.
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  4. #4
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    Hello, hoanghai549!

    \text{If }y\,=\, \arctan x\,\text{ and }\,x<0,\,\text{ then }y\text{ lies in what quadrant?}

    We have: . y\,=\,\arctan x \quad\Rightarrow\quad \tan y \,=\,x\;\;\text{ and }x\text{ is negative.}

    The tangent function is negative in Quadrants 2 and 4.

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  5. #5
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    Cool

    Quote Originally Posted by Soroban View Post
    Hello, hoanghai549!


    We have: . y\,=\,\arctan x \quad\Rightarrow\quad \tan y \,=\,x\;\;\text{ and }x\text{ is negative.}

    The tangent function is negative in Quadrants 2 and 4.
    Could you elaborate it in detail ? I have confused on it .
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