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The slope angle  of any line in
 is the angle between the line and  -axis; in the case that the line is descending, the angle is negative. We always have that
 .
For all non-vertical lines having a slope of  , the slope angle is
and we also have that
Below are some examples of slope angles of lines that intersect the  -axis.
In some mathematical works, the slope angle of a line in
 is defined to be the angle measured from the positive  -axis to the line in the counterclockwise direction. This definition has some drawbacks because slope angles are then allowed to be obtuse but can no longer be negative. When this definition is used, the formula
 no longer holds. The convention in PlanetMath is to use the former definition.
- 1
- ``Slope, Distance and Equation Calculator.'' 1729 Software Systems. Accessed on 24 June 2007. URL: http://www.1728.com/distance.htm
- 2
- ``Slope angle.'' McGraw-Hill Dictionary of Scientific and Technical Terms. McGraw-Hill Companies, Inc., 2003. Accessed via Answers.com on 7 June 2007. URL: http://www.answers.com/topic/slope-angle
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"slope angle" is owned by Wkbj79. [ full author list (3) ]
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(view preamble)
Cross-references: PlanetMath, obtuse, positive, intersect, slope, negative, angle, line
There are 9 references to this entry.
This is version 19 of slope angle, born on 2007-06-07, modified 2007-06-27.
Object id is 9546, canonical name is SlopeAngle.
Accessed 1907 times total.
Classification:
| AMS MSC: | 51N20 (Geometry :: Analytic and descriptive geometry :: Euclidean analytic geometry) | | | 53A04 (Differential geometry :: Classical differential geometry :: Curves in Euclidean space) |
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Pending Errata and Addenda
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{.} \rput[a](1,3){.} \rput[b](7,-3){... ...positive \,}\alpha$} \rput(3.5,-2.5){$\mbox{negative \,}\alpha$} \end{pspicture}](http://images.planetmath.org:8080/cache/objects/9546/l2h/img9.png "\begin{pspicture}(-7,-3)(7,3) \rput[l](-7,0){.} \rput[a](1,3){.} \rput[b](7,-3){... ...positive \,}\alpha$} \rput(3.5,-2.5){$\mbox{negative \,}\alpha$} \end{pspicture}")