document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157260>Question 157260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In studying the emission of light, in order to determine the angle at which the intensity is a giving value, the equation sin^2(A) - 4sin(A) + 1 = 0  must be solved.  Find the angle A (to 0.1 of a degree).  (sin^2(A) = (sinA)^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115975 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=115975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28A%29-4sin%28A%29%2B1=0 ALIGN=MIDDLE  ALT=\"sin%5E2%28A%29-4sin%28A%29%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks like a quadratic equation in disguise.<BR>\n" );
document.write( "Let's substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=sin%28A%29 ALIGN=MIDDLE  ALT=\"u=sin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28A%29-4sin%28A%29%2B1=0 ALIGN=MIDDLE  ALT=\"sin%5E2%28A%29-4sin%28A%29%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2-4u%2B1=0 ALIGN=MIDDLE  ALT=\"u%5E2-4u%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the quadratic formula, solve for u.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"u+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%284+%2B-+sqrt%28+16-4+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u+=+%284+%2B-+sqrt%28+16-4+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%284+%2B-+sqrt%28+12%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u+=+%284+%2B-+sqrt%28+12%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D+=+%284+%2B+sqrt%28+12%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B1%5D+=+%284+%2B+sqrt%28+12%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D+=+%284+%2B+3.46%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B1%5D+=+%284+%2B+3.46%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D+=+%287.46%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B1%5D+=+%287.46%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D+=+3.73+ ALIGN=MIDDLE  ALT=\"u%5B1%5D+=+3.73+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=sin%28A%29 ALIGN=MIDDLE  ALT=\"u=sin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D+=+3.73+ ALIGN=MIDDLE  ALT=\"u%5B1%5D+=+3.73+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29+=+3.73+ ALIGN=MIDDLE  ALT=\"sin%28A%29+=+3.73+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We throw this solution out since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28sin%28A%29%29%3C=1 ALIGN=MIDDLE  ALT=\"abs%28sin%28A%29%29%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=%284+-+sqrt%28+12%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B2%5D=%284+-+sqrt%28+12%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=%284+-+3.46%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B2%5D=%284+-+3.46%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=%280.54%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"u%5B2%5D=%280.54%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=0.27 ALIGN=MIDDLE  ALT=\"u%5B2%5D=0.27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=sin%28A%29 ALIGN=MIDDLE  ALT=\"u=sin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D=0.27 ALIGN=MIDDLE  ALT=\"u%5B2%5D=0.27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=0.27 ALIGN=MIDDLE  ALT=\"sin%28A%29=0.27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+sin%5E%28-1%29%280.27%29+ ALIGN=MIDDLE  ALT=\"A=+sin%5E%28-1%29%280.27%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=15.6 ALIGN=MIDDLE  ALT=\"A=15.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and by identity,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=180-15.6=164.4 ALIGN=MIDDLE  ALT=\"A=180-15.6=164.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );