Identities Following From The Definitions

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node59.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node59.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node61.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node60.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H2>Identities Following From The Definitions</H2> <P> As you may or may not have already noticed, it is the case that each trig function is the reciprocal of some other trig function. We note these identities as follows: <P> <CENTER> <IMG WIDTH=239 HEIGHT=132 ALIGN=BOTTOM ALT="[identities]" SRC="img170.gif"> </CENTER> <P> Moreover, it is true that all of the trigonometric functions can be written in terms of <IMG WIDTH=29 HEIGHT=12 ALIGN=BOTTOM ALT="sin(theta)" SRC="img86.gif"> and <IMG WIDTH=30 HEIGHT=12 ALIGN=BOTTOM ALT="cos(theta)" SRC="img84.gif">, which means that we can easily determine the values of all six trig functions as long as we can determine just two of them. Note the following: <P> <CENTER> <IMG WIDTH=237 HEIGHT=89 ALIGN=BOTTOM ALT="[identities]" SRC="img171.gif"> </CENTER> <P> <HR><center> <table border=1> <td><A HREF="node59.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node59.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node61.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node60.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>