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Finding the angle given positive x component and negative y component

  1. Sep 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Ax = 3m
    Ay = -4m

    Find the angle with respect to the x axis


    2. Relevant equations
    Tan = Ay/Ax


    3. The attempt at a solution
    Tan = Ay/Ax
    = -4m/3m
    = 1.333333
    angle = -53 degrees

    Is -53 degrees a correct answer or should it be positive 53?
     
  2. jcsd
  3. Sep 17, 2013 #2

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    Hello hey123a,

    Welcome to Physics Forums!

    I'd tell you, but I think you might be able to determine this one on your own by first plotting the vector on a graph. Even a piece of scratch paper or a paper napkin should be enough for this.

    First plot the x- and y-axes.

    Then place the vector on the graph, with its tail at the origin and its head at point (3 m, -4 m).

    The angle is with respect to the positive x-axis.

    Positive angles (with 0o < θ < 180o) represent a vector that is above the x-axis. Negative angles (with -180o < θ < 0o) represent a vector below the x-axis.
     
  4. Sep 17, 2013 #3
    Hey thank you for the greeting, i'll definitely be around the forums a lot because physics is one of the subjects that i don't feel confident in.

    Well, I placed the vector on the graph and it is definitely below the positive x axis, so, my conclusion is that the answer is -53 degrees
     
  5. Sep 17, 2013 #4

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    Sounds good to me! :smile:
     
  6. Sep 17, 2013 #5

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    As a heads up though, for future problems, you might want to get into the habit of actually plotting the vectors out. You can't blindly trust the inverse trigonometric functions on your calculator, as they can mislead you.

    For example, suppose Ax was -3 m instead of positive 3 m.

    The angle you first calculate is θ = ATAN(-4/-3) = 53o.

    The angle you calculate is positive, but you can tell when graphing the vector that not only is the angle negative, but it also is in the third quadrant. In that case you need to subtract 180o from the result. So in that case the angle would be 53o - 180o = -127o.

    -------------------------------------------

    As another example, suppose that the signs of both were opposite what you were given,
    Ax = -3
    Ay = 4

    The angle you calculate with the ATAN function gives you -53o again (this is the same result as in the original problem). But you can tell by graphing the function that its in the second quadrant. So now you need to add 180o to it, making it the correct +127o.
     
  7. Sep 17, 2013 #6
    Thank you for taking the time out of your schedule to help me out. I really appreciate it! :smile:
    I pressed that thank you button on your post which I found pretty neat
     
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