document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156563>Question 1156563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \cos\theta-\sqrt{3}\sin\theta=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779296 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Don't use that format to present the problem and make us guess what it is...!<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29-sqrt%283%29sin%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"cos%28theta%29-sqrt%283%29sin%28theta%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In an equation involving sin(theta) and cos(theta), at some point we are almost certainly going to use sin^2+cos^2=1 to get the equation in either sine or cosine alone.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29+=+1%2Bsqrt%283%29sin%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29+=+1%2Bsqrt%283%29sin%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=cos%5E2%28theta%29+=+1%2B2sqrt%283%29sin%28theta%29%2B3sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29+=+1%2B2sqrt%283%29sin%28theta%29%2B3sin%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=1-sin%5E2%28theta%29+=+1%2B2sqrt%283%29sin%28theta%29%2B3sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"1-sin%5E2%28theta%29+=+1%2B2sqrt%283%29sin%28theta%29%2B3sin%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=0+=+4sin%5E2%28theta%29%2B2sqrt%283%29sin%28theta%29 ALIGN=MIDDLE  ALT=\"0+=+4sin%5E2%28theta%29%2B2sqrt%283%29sin%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=0+=+sin%28theta%29%284sin%28theta%29%2B2sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"0+=+sin%28theta%29%284sin%28theta%29%2B2sqrt%283%29%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+=+0 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+0 ALIGN=MIDDLE  ALT=\"theta+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+%284%2F3%29pi ALIGN=MIDDLE  ALT=\"theta+=+%284%2F3%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+%285%2F3%29pi ALIGN=MIDDLE  ALT=\"theta+=+%285%2F3%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "At one point in our work we squared both sides of the equation; so we need to check for extraneous solutions.<br><BR>\n" );
document.write( "theta = 0:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%280%29=+1 ALIGN=MIDDLE  ALT=\"cos%280%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%283%29sin%280%29+=+1 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%283%29sin%280%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  YES<br><BR>\n" );
document.write( "theta = (4/3)pi:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28%284%2F3%29pi%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"cos%28%284%2F3%29pi%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%283%29sin%28%284%2F3%29pi%29+=+1%2Bsqrt%283%29%28-sqrt%283%29%2F2%29+=+1-3%2F2+=+-1%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  YES<br><BR>\n" );
document.write( "theta = (5/3)pi:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28%285%2F3%29pi%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"cos%28%285%2F3%29pi%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%283%29sin%28%285%2F3%29pi%29+=+1-sqrt%283%29%28-sqrt%283%29%2F2%29+=+1-3%2F2+=+-1%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  NO<br><BR>\n" );
document.write( "ANSWER: theta = 0; theta = (-4/3)pi<br><BR>\n" );
document.write( "A graph of cos(theta)-sqrt(3)sin(theta)-1, showing zeros at 0 and (4/3)pi:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-pi%2F2%2C5pi%2F2%2C-4%2C2%2Ccos%28x%29-sqrt%283%29sin%28x%29-1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-pi%2F2%2C5pi%2F2%2C-4%2C2%2Ccos%28x%29-sqrt%283%29sin%28x%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );