What is an angle exactly?

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node8.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node8.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node10.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node9.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H2>What is an <B>angle</B> exactly?</H2> <P> We begin this section with the definition of an angle, which will involve several terms and their definitions. An <B>angle</B> is a portion of the 2-dimensional plane which resides between two different directed line segments. The starting position of the angle is known as the <B>initial side</B> and the ending position of the angle is known as the <B>terminal side</B>. The point from which both of the directed line segments originate is known as the <B>vertex</B> of the angle. See the figure below for a visual example of an angle. <P> <CENTER> <IMG SRC="p3-1.gif" ALT="[angle diagram]" WIDTH=178 HEIGHT=147><P> </CENTER> <P> We will say an angle is in <B>standard position</B> if its initial side lies on the positive <I>x</I>-axis. Moreover, we will say that angles which are spanned in a counterclockwise motion are <B>positive</B>, while angles which are spanned in a clockwise fashion will be called <B>negative</B>. See the next two figures. <P> <CENTER> <IMG SRC="p3-2a.gif" ALT="[positive angle]" WIDTH=273 HEIGHT=142><P> <IMG SRC="p3-2b.gif" ALT="[negative angle]" WIDTH=242 HEIGHT=142><P> </CENTER> <P> One quick ``note on notation'' is useful here. We will often use Greek letters to denote angles, such as <IMG WIDTH=6 HEIGHT=12 ALIGN=BOTTOM ALT="theta" SRC="img1.gif">, <IMG WIDTH=7 HEIGHT=7 ALIGN=BOTTOM ALT="alpha" SRC="img2.gif">, and <IMG WIDTH=9 HEIGHT=24 ALIGN=MIDDLE ALT="beta" SRC="img3.gif">. <P> One final note in this section, which will deal with the measurement of angles. There are two such types of measurement; they deal with <B>degrees</B> and <B>radians</B>. We will not go into the details of these two types of measurement at this time. For now, the reader must realize that we will be using both sets of units throughout this material. Thus, it is imperative that you grow comfortable with both systems, especially in the area of converting from one unit system to another. This brings us to our next section. <P> <HR><center> <table border=1> <td><A HREF="node8.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node8.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node10.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node9.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A HREF="http://www.math.psu.edu/sellersj/">James A. Sellers</A> </I> </ADDRESS> </BODY>