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Revision difference : slope angle |
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Version 5 |
| \PMlinkescapeword{axis} |
\PMlinkescapeword{axis} |
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| 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 $\{(x,y) \in \ell : y \ge 0 \}$ and $\{(x,0): x \ge 0 \}$. |
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 $\{(x,y) \in \ell : y \ge 0 \}$ and $\{(x,0): x \ge 0 \}$. |
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| In the following pictures, the $x$ axis is drawn in red, and the slope angle is marked with an arc. |
In the following pictures, the $x$ axis is drawn in red, and the slope angle is marked with an arc. |
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| \begin{center} |
\begin{center} |
| \begin{pspicture}(-7,-3)(7,3) |
\begin{pspicture}(-7,-3)(7,3) |
| \psline[linecolor=red]{<->}(-7,0)(-1,0) |
\psline[linecolor=red]{<->}(-7,0)(-1,0) |
| \psline[linecolor=red]{<->}(1,0)(7,0) |
\psline[linecolor=red]{<->}(1,0)(7,0) |
| \psline{<->}(-7,-2)(-1,2) |
\psline{<->}(-7,-2)(-1,2) |
| \psarc(-4,0){0.5}{0}{33.69} |
\psarc(-4,0){0.5}{0}{33.69} |
| \psline{<->}(1,3)(7,-3) |
\psline{<->}(1,3)(7,-3) |
| \psarc(4,0){0.5}{0}{135} |
\psarc(4,0){0.5}{0}{135} |
| \end{pspicture} |
\end{pspicture} |
| \end{center} |
\end{center} |
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| If the slope angle of a line $\ell$ has an angle measure of $\theta$, then the slope of $\ell$ is $m=\arctan\theta$. |
If the slope angle of a line $\ell$ has an angle measure of $\theta$, then the slope of $\ell$ is $m=\arctan\theta$. |
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| \begin{thebibliography}{9} |
\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} |
\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} |
\end{thebibliography} |
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