Trig Functions of Any Angle - The Generalization

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node26.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="trig.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node28.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node27.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H1>Trig Functions of Any Angle - The Generalization</H1> <P> We have now seen how to define the six trig functions for any acute angle in standard representation whose terminal side resides within Quadrant I of the plane. (Recall that the plane can be broken into four quadrants, as denoted below.) <P> <CENTER> <IMG SRC="p8-1.gif" ALT="[diagram of the 4 quadrants]" WIDTH=213 HEIGHT=142> </CENTER> <P> So, we can determine the trig value of an acute angle at this point. Now we need to generalize our work so that we can handle ANY angle, whether it be larger than 90° or be negative, to name a couple of the types of angles with which we still cannot work. To obtain this generalization, we need the concept of a reference angle. <P> <HR> <CENTER> <TABLE BORDER=1> <td><A HREF="node26.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="trig.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node28.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node27.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>