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'slope angle'
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| Title of object: |
slope angle |
| Canonical Name: |
SlopeAngle |
| Type: |
Definition |
| Created on: |
2007-06-07 03:18:04 |
| Modified on: |
2007-06-07 06:56:57 |
| Classification: |
msc:51N20, msc:53A04 |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{pstricks}
\usepackage{psfrag}
\usepackage{graphicx}
\usepackage{amsthm}
\usepackage{xypic}
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Content:
\PMlinkescapeword{axis}
\PMlinkescapeword{right}
Let $\ell$ be a line in $\mathbb{R}^2$ that is not of the form $y=c$ for some $c \in \mathbb{R}$. Let $t \in \mathbb{R}$ such that $\ell$ and the $x$ axis intersect at $(t,0)$. The \emph{slope angle} of $\ell$ is the angle formed by the rays $\{(x,y) \in \ell : y \ge 0 \}$ (the portion of the line $\ell$ above the $x$ axis) and $\{(x,0): x \ge t \}$ (the portion of the $x$ axis to the right of $(t,0)$).
In the following pictures, the $x$ axis is drawn in red, the two colored line in the left portion of the picture is $\ell_1$, and the two colored line in the right portion of the picture. The rays $\{(x,y) \in \ell_1 : y \ge 0 \}$ and $\{(x,y) \in \ell_2 : y \ge 0 \}$ are drawn in blue, and the slope angle is marked with an arc.
\begin{center}
\begin{pspicture}(-7,-3)(7,3)
\psline[linecolor=red]{<->}(-7,0)(-1,0)
\psline[linecolor=red]{<->}(1,0)(7,0)
\psline{<-*}(-7,-2)(-4,0)
\psline[linecolor=blue]{*->}(-4,0)(-1,2)
\psarc(-4,0){0.5}{0}{33.69}
\psline[linecolor=blue]{<-*}(1,3)(4,0)
\psline{*->}(4,0)(7,-3)
\psarc(4,0){0.5}{0}{135}
\psdots(-4,0)(4,0)
\end{pspicture}
\end{center}
If the slope angle of a line $\ell$ has an angle measure of $\theta \neq \frac{\pi}{2}$, then the slope of $\ell$ is $m=\tan\theta$.
\begin{thebibliography}{9}
\bibitem{mcgrawhill} ``Slope angle.'' \emph{McGraw-Hill Dictionary of Scientific and Technical Terms.} McGraw-Hill Companies, Inc., 2003. Accessed via Answers.com on 07 June 2007. URL: \PMlinkexternal{http://www.answers.com/topic/slope-angle}{http://www.answers.com/topic/slope-angle}
\end{thebibliography} |
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