Graphs of the Trigonometric Functions

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node43.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="node45.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node44.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H1>Graphs of the Trigonometric Functions</H1> <P> As is the case with most subjects in mathematics, we desire a visual approach to this subject. Indeed, it would be nice to be able to draw the graphs of the functions we have been studying. <P> A preliminary study of this begins with simply plotting some of the points and ``connecting the dots.'' If one goes through this exercise, the task of drawing these curves is fairly straightforward. In order to accomplish, recall the following values of the trig functions: <P> <CENTER> <TABLE BORDER CELLPADDING=6> <TR VALIGN=BOTTOM> <TD ALIGN=center><IMG WIDTH=93 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img1.gif"></TD> <TD ALIGN=center><IMG WIDTH=93 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img2.gif"></TD> <TD ALIGN=center><IMG WIDTH=34 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img3.gif"></TD> <TD ALIGN=center><IMG WIDTH=36 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img4.gif"></TD> <TD ALIGN=center><IMG WIDTH=39 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img5.gif"></TD> <TD ALIGN=center><IMG WIDTH=35 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img6.gif"></TD> <TD ALIGN=center><IMG WIDTH=35 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img7.gif"></TD> <TD ALIGN=center><IMG WIDTH=36 HEIGHT=14 ALIGN=BOTTOM ALT="" SRC="tables/img8.gif"></TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>0°</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>und</TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>30°</TD> <TD ALIGN=center><IMG WIDTH=9 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img10.gif"> </TD> <TD ALIGN=center><IMG WIDTH=8 HEIGHT=24 ALIGN=MIDDLE ALT="" SRC="tables/img11.gif"> </TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img12.gif"> </TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img13.gif"></TD> <TD ALIGN=center>2</TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img14.gif"> </TD> <TD ALIGN=center><IMG WIDTH=24 HEIGHT=20 ALIGN=MIDDLE ALT="" SRC="tables/img15.gif"></TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>45°</TD> <TD ALIGN=center><IMG WIDTH=9 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img17.gif"> </TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img18.gif"></TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img18.gif"></TD> <TD ALIGN=center>1</TD> <TD ALIGN=center><IMG WIDTH=24 HEIGHT=20 ALIGN=MIDDLE ALT="" SRC="tables/img19.gif"></TD> <TD ALIGN=center><IMG WIDTH=24 HEIGHT=20 ALIGN=MIDDLE ALT="" SRC="tables/img19.gif"></TD> <TD ALIGN=center>1</TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>60°</TD> <TD ALIGN=center><IMG WIDTH=9 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img21.gif"> </TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img12.gif"></TD> <TD ALIGN=center><IMG WIDTH=8 HEIGHT=24 ALIGN=MIDDLE ALT="" SRC="tables/img11.gif"> </TD> <TD ALIGN=center><IMG WIDTH=24 HEIGHT=20 ALIGN=MIDDLE ALT="" SRC="tables/img15.gif"></TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img14.gif"></TD> <TD ALIGN=center>2</TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=27 ALIGN=MIDDLE ALT="" SRC="tables/img13.gif"></TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>90°</TD> <TD ALIGN=center><IMG WIDTH=9 HEIGHT=21 ALIGN=MIDDLE ALT="" SRC="tables/img24.gif"> </TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>0</TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>180°</TD> <TD ALIGN=center><IMG WIDTH=9 HEIGHT=9 ALIGN=BOTTOM ALT="" SRC="tables/img26.gif"> </TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>-1</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>-1</TD> <TD ALIGN=center>und</TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>270°</TD> <TD ALIGN=center><IMG WIDTH=16 HEIGHT=24 ALIGN=MIDDLE ALT="" SRC="tables/img28.gif"> </TD> <TD ALIGN=center>-1</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>-1</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>0</TD> </TR> <TR VALIGN=BOTTOM> <TD ALIGN=center>360°</TD> <TD ALIGN=center><IMG WIDTH=19 HEIGHT=13 ALIGN=BOTTOM ALT="" SRC="tables/img33.gif"> </TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>0</TD> <TD ALIGN=center>und</TD> <TD ALIGN=center>1</TD> <TD ALIGN=center>und</TD> </TR> </TABLE> </CENTER> <P> <HR><center> <table border=1> <td><A HREF="node43.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="node45.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node44.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>