document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073641>Question 1073641</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this problem .\r<BR>\n" );
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document.write( "Find the Cartesian coordinates of the given point.\r<BR>\n" );
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document.write( "(&#8730;3,pi/6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688478 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to find the Cartesian coordinates of a point<BR>\n" );
document.write( "a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%283%29 ALIGN=MIDDLE  ALT=\"r=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the origin,<BR>\n" );
document.write( "along a line forming an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=pi%2F6 ALIGN=MIDDLE  ALT=\"theta=pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the positive x-axis.<BR>\n" );
document.write( " <BR>\n" );
document.write( "A full turn is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "An angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=pi%2F6 ALIGN=MIDDLE  ALT=\"theta=pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C2%2C-2%2C2%2Cgrid%280%29%2C%0D%0Acircle%280%2C0%2Csqrt%283%29%29%2Ctriangle%280%2C0%2Csqrt%283%29%2F2%2C1.5%2Csqrt%283%29%2F2%2C0%29%2C%0D%0Atriangle%28sqrt%283%29%2C0%2Csqrt%283%29%2F2%2C1.5%2Csqrt%283%29%2F2%2C0%29%2C%0D%0Arectangle%280.866%2C0%2C0.766%2C0.1%29%2C%0D%0Atriangle%280%2C0%2Csqrt%283%29%2F2%2C1.5%2C-sqrt%283%29%2F2%2C1.5%29%2C%0D%0Atriangle%280%2C0%2C-sqrt%283%29%2F2%2C1.5%2C-sqrt%283%29%2C0%29%2C%0D%0Atriangle%280%2C0%2C-sqrt%283%29%2F2%2C-1.5%2C-sqrt%283%29%2C0%29%2C%0D%0Atriangle%280%2C0%2C-sqrt%283%29%2F2%2C-1.5%2Csqrt%283%29%2F2%2C-1.5%29%2C%0D%0Atriangle%280%2C0%2Csqrt%283%29%2C0%2Csqrt%283%29%2F2%2C-1.5%29%2C%0D%0Acircle%28sqrt%283%29%2F2%2C1.5%2C0.05%29%2Clocate%280.92%2C1.7%2CP%28x%2Cy%29%29%2C%0D%0Alocate%280.766%2C0%2CQ%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > You know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=OP=sqrt%283%29 ALIGN=MIDDLE  ALT=\"r=OP=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=angle ALIGN=MIDDLE  ALT=\"theta=angle\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QOP=pi%2F6 ALIGN=MIDDLE  ALT=\"QOP=pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and you need to find the lengths of OQ and PQ,<BR>\n" );
document.write( "the legs of right triangle OPQ.<BR>\n" );
document.write( "Maybe you remember that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F6%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F6%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F6%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F6%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If you also remember trigonometric ratios and \"SOHCAHTOA\",<BR>\n" );
document.write( "you can apply all that to right triangle OPQ,<BR>\n" );
document.write( "and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=OQ ALIGN=MIDDLE  ALT=\"x=OQ\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=PQ ALIGN=MIDDLE  ALT=\"y=PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If you don't, maybe you remember the Pythagorean theorem.<BR>\n" );
document.write( "Triangle OPQ is half of an equilateral triangle,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=OQ=%281%2F2%29OP=highlight%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=OQ=%281%2F2%29OP=highlight%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The Pythagorean theorem, applied to OPQ says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OQ%5E2%2BPQ%5E2=OP%5E2 ALIGN=MIDDLE  ALT=\"OQ%5E2%2BPQ%5E2=OP%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting what you know, you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29%5E2%2BPQ%5E2=%28sqrt%283%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%29%5E2%2BPQ%5E2=%28sqrt%283%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%29%5E2%2F2%5E2%2BPQ%5E2=3 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%29%5E2%2F2%5E2%2BPQ%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4%2BPQ%5E2=3 ALIGN=MIDDLE  ALT=\"3%2F4%2BPQ%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2=3-3%2F4 ALIGN=MIDDLE  ALT=\"PQ%5E2=3-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2=9%2F4 ALIGN=MIDDLE  ALT=\"PQ%5E2=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ=sqrt%289%2F4%29 ALIGN=MIDDLE  ALT=\"PQ=sqrt%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=PQ=highlight%283%2F2%29 ALIGN=MIDDLE  ALT=\"y=PQ=highlight%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the Cartesian coordinates are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=sqrt%283%29%2F2%2Cy=3%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=sqrt%283%29%2F2%2Cy=3%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or for an approximate x value, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=0.866%2Cy=1.5%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=0.866%2Cy=1.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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