document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074693>Question 1074693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line with equation y + 2x = 0 coincides with the terminal side of an angle &#952; in standard position in Quadrant IV .\r<BR>\n" );
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document.write( "What is the value of tan0?\r<BR>\n" );
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document.write( "The line with equation &#8722;a+3b=0 coincides with the terminal side of an angle &#952; in standard position and sin&#8201;&#952;<0 .\r<BR>\n" );
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document.write( "What is the value of cos&#952; ?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689387 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=689387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2x=0 ALIGN=MIDDLE  ALT=\"y%2B2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-1.1%2C1.3%2C-1.2%2C1.2%2Cgrid%280%29%2C%0D%0Ared%28circle%280%2C0%2C1%29%29%2Clocate%280.35%2C-0.6%2Cblue%28y%2B2x=0%29%29%2C%0D%0Ablue%28line%28-1%2C2%2C1%2C-2%29%29%2Carrow%280%2C0%2C1.2%2C0%29%2C%0D%0Aarrow%280%2C0%2C0.577%2C-1.155%29%2Ccircle%280.447%2C-.894%2C0.02%29%2C%0D%0Aarc%280%2C0%2C0.6%2C0.6%2C63.4%2C360%29%2Clocate%280.23%2C0.25%2Ctheta%29%2C%0D%0Alocate%280.465%2C-0.89%2CP%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Maybe your teacher instructor defined trigonometric functions<BR>\n" );
document.write( "based on the coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%5BP%5D%2Cy%5BP%5D%29 ALIGN=MIDDLE  ALT=\"P%28x%5BP%5D%2Cy%5BP%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28cos%28theta%29=x%5BP%5D%2Csin%28theta%29=y%5BP%5D%2Ctan%28theta%29=y%5BP%5D%2Fx%5BP%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "My 9th grade math teacher defined <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=than%28theta%29=y%5BQ%5D ALIGN=MIDDLE  ALT=\"than%28theta%29=y%5BQ%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28280%2C420%2C-1.1%2C1.3%2C-2.3%2C1.3%2Cgrid%280%29%2C%0D%0Ared%28circle%280%2C0%2C1%29%29%2Clocate%280.35%2C-0.6%2Cblue%28y%2B2x=0%29%29%2C%0D%0Ablue%28line%28-1%2C2%2C1.5%2C-3%29%29%2Carrow%280%2C0%2C1.2%2C0%29%2C%0D%0Aarrow%280%2C0%2C0.577%2C-1.155%29%2Cblue%28triangle%280%2C0%2C1%2C0%2C1%2C-2%29%29%2C%0D%0Ablue%28rectangle%281%2C0%2C0.9%2C-0.1%29%29%2C%0D%0Aarc%280%2C0%2C0.6%2C0.6%2C63.4%2C360%29%2Clocate%280.23%2C0.25%2Ctheta%29%2C%0D%0Alocate%281.05%2C-1.95%2CQ%29%2Ccircle%281%2C-2%2C0.03%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Either way it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=y%5BR%5D%2Fx%5BR%5D ALIGN=MIDDLE  ALT=\"tan%28theta%29=y%5BR%5D%2Fx%5BR%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%5BR%5D%2Cy%5BR%5D%29 ALIGN=MIDDLE  ALT=\"R%28x%5BR%5D%2Cy%5BR%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "on that blue line that passes through the origin <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%280%2C0%29 ALIGN=MIDDLE  ALT=\"O%280%2C0%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%2B2x=0 ALIGN=MIDDLE  ALT=\"y%2B2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x ALIGN=MIDDLE  ALT=\"y=-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of course that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=y%5BR%5D%2Fx%5BR%5D=%28y%5BR%5D-0%29%2F%28x%5BR%5D-0%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=y%5BR%5D%2Fx%5BR%5D=%28y%5BR%5D-0%29%2F%28x%5BR%5D-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope of the line,<BR>\n" );
document.write( "and the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x ALIGN=MIDDLE  ALT=\"y=-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in the slope-intercept form of the equation of the line.<BR>\n" );
document.write( " <BR>\n" );
document.write( "1) Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2B3b=0 ALIGN=MIDDLE  ALT=\"-a%2B3b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would have to be graphed on a pait if a-b axes.<BR>\n" );
document.write( "I would use the usual x-y axes and say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system+%28a=x%2Cb=y%29 ALIGN=MIDDLE  ALT=\"system+%28a=x%2Cb=y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, the line would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B3y=0 ALIGN=MIDDLE  ALT=\"-x%2B3y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x ALIGN=MIDDLE  ALT=\"3y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=1%2F3 ALIGN=MIDDLE  ALT=\"tan%28theta%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%3E0 ALIGN=MIDDLE  ALT=\"sin%28theta%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=sqrt%281-cos%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29=sqrt%281-cos%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-cos%5E2%28theta%29%29%2Fcos%28theta%29=1%2F3 ALIGN=MIDDLE  ALT=\"sqrt%281-cos%5E2%28theta%29%29%2Fcos%28theta%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-cos%5E2%28theta%29%29=cos%28theta%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%281-cos%5E2%28theta%29%29=cos%28theta%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-cos%5E2%28theta%29=cos%5E2%28theta%29%2F9 ALIGN=MIDDLE  ALT=\"1-cos%5E2%28theta%29=cos%5E2%28theta%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-9cos%5E2%28theta%29=cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"9-9cos%5E2%28theta%29=cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=10cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"9=10cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F10=cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"9%2F10=cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=sqrt%281-9%2F10%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29=sqrt%281-9%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=sqrt%281%2F10%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29=sqrt%281%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sin%28theta%29=sqrt%2810%29%2F10%29 ALIGN=MIDDLE  ALT=\"highlight%28sin%28theta%29=sqrt%2810%29%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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