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Math Help - getting wrong theta from tan(theta)=-4/3

  1. #1
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    getting wrong theta from tan(theta)=-4/3

    The exercise asks, convert (-3,4) to polar coordinates.
    I get (5, -4.140), but it's wrong. The solution is supposed to be (5, 2.21) or (-5, 5.36).

    Why do I keep getting the wrong answer?

    Thanks,
    Ivy
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  2. #2
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    (-5, 5.36) could not possibly be right, a radius length can only ever be positive...

    Anyway, \displaystyle r = \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.

    Now, notice that (-3, 4) is in the second quadrant, so \displaystyle \theta = \pi - \arctan{\left(\frac{4}{3}\right)}.
    Last edited by Prove It; May 16th 2011 at 08:52 AM.
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  3. #3
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    Hello, Ivy!

    Sorry, Prove it . . . r can be negative.


    Convert (-3,4) to polar coordinates.

    I get (5, -4.140), but it's wrong.
    The solution is supposed to be (5, 2.21) or (-5, 5.36).

    Why do I keep getting the wrong answer?
    . . How did you get that angle?
    Code:
           (-3,4) |
              *   |
              :\  |
             4: \5|
              :  \|
          - - + - + - - - -
                3 |

    We see that: . r \,=\,5.

    The angle is: . \theta \:=\:\tan^{-1}\left(\text{-}\tfrac{4}{3}\right) \:\approx\:\text{-}0.927\text{ radians}

    This translates to positive angles of: . 2.21\text{ and }5.36\text{ radians.}


    You should be aware that there are an infinite number of ways
    . . to designate a point in polar coordinates.

    Two of the ways are: . (2.21,\,5) and (-5,\,5.36)


    Recall how polar coordinates are plotted.


    The first (5,\,2,21) tells us:
    . . stand at the pole (origin), face East, turn 2.21 radians CCW
    . . and walk forward 5 units.
    This places us at the point in Quadrant 2.

    The second (-5,\,5.36) tells us:
    . . stand at the pole, face East, turn 5.36 radians CCW
    . . and walk backward 5 units.
    This places us at the same point.

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  4. #4
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    Thank you so much. I get confused about when to use my calculator in radians or degrees mode. Do polar coordinates require that theta always be in rads instead of degrees? When I take the trig. ratio of two sides, will the answer always be in rads?
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