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Homework Help: Finding Angle of Inclination With a Given Slope

  1. Mar 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the angle of inclination of a line when the slope, m, is equal to -1/2

    2. Relevant equations
    m = rise/run = tan(φ)

    φ=angle of inclination

    3. The attempt at a solution

    I thought the answer would simply be using arctan on the slope, but my answer gives me -26.565051 degrees when the answer is supposed to be 153 degrees:

    arctan(-1/2) = 26.565051
  2. jcsd
  3. Mar 28, 2016 #2


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    Gold Member

    yes, in fact ## 180°-26,6°=153,4° ## it is the same angle... (remember that the period of the tangent is ##\pi##)
  4. Mar 28, 2016 #3
    Ahhh, thank you! I've been scratching my head at this for a few days now. I dont think the Calculus text Im using(Anton Calculus 6th ed.) ever talked about the period of the tangent being π. Or I somehow missed it.
  5. Mar 28, 2016 #4


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    Science Advisor
    Homework Helper
    Gold Member

    Remember that the arctan function on a calculator gives answers in the principal value range, ##(-\frac \pi 2,\frac \pi 2)##, but the angle of inclination of a line is between ##0## and ##\pi##. That's why you need the second quadrant angle.
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