document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868504>Question 868504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is ridiculously confusing to me, any help is greatly appreciated!\r<BR>\n" );
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document.write( "If it is known that sin a = 4/5, pi/2 < a < pi\r<BR>\n" );
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document.write( "and that sin b = - (2 * sqrt(5) / 5), pi < b < 3pi/2,\r<BR>\n" );
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document.write( "find the exact value of cos( a + b )\r<BR>\n" );
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document.write( "Pretty please help me out, i'm in a crunch right now :/ thanks though :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523592 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=523592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From trig relation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%2Bb%29=cos%28a%29cos%28b%29-sin%28a%29sin%28b%29 ALIGN=MIDDLE  ALT=\"cos%28a%2Bb%29=cos%28a%29cos%28b%29-sin%28a%29sin%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So you need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29 ALIGN=MIDDLE  ALT=\"cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28b%29 ALIGN=MIDDLE  ALT=\"cos%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28a%29%2Bsin%5E2%28a%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28a%29%2Bsin%5E2%28a%29=1\"   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=cos%5E2%28a%29%2B%284%2F5%29%5E2=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28a%29%2B%284%2F5%29%5E2=1\"   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%28a%29=25%2F25-16%2F25 ALIGN=MIDDLE  ALT=\"cos%5E2%28a%29=25%2F25-16%2F25\"   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%28a%29=9%2F25 ALIGN=MIDDLE  ALT=\"cos%5E2%28a%29=9%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29=0+%2B-+3%2F5 ALIGN=MIDDLE  ALT=\"cos%28a%29=0+%2B-+3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since you're given information that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2%3Ca%3Cpi ALIGN=MIDDLE  ALT=\"pi%2F2%3Ca%3Cpi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29 ALIGN=MIDDLE  ALT=\"cos%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be negative (2nd quadrant) so you choose,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29=-3%2F5 ALIGN=MIDDLE  ALT=\"cos%28a%29=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Same thing,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28b%29%2Bsin%5E2%28b%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28b%29%2Bsin%5E2%28b%29=1\"   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%28b%29%2B%28-%282sqrt%285%29%29%2F5%29%5E2=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28b%29%2B%28-%282sqrt%285%29%29%2F5%29%5E2=1\"   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%28b%29%2B%284%2F5%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28b%29%2B%284%2F5%29=1\"   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%28b%29=5%2F5-4%2F5 ALIGN=MIDDLE  ALT=\"cos%5E2%28b%29=5%2F5-4%2F5\"   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%28b%29=1%2F5 ALIGN=MIDDLE  ALT=\"cos%5E2%28b%29=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28b%29=0+%2B-+sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28b%29=0+%2B-+sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the information, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > lies in the 3rd quadrant, where the cosine is also negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28b%29=-sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28b%29=-sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now go back to the original equation and plug in the values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%2Bb%29=cos%28a%29cos%28b%29-sin%28a%29sin%28b%29 ALIGN=MIDDLE  ALT=\"cos%28a%2Bb%29=cos%28a%29cos%28b%29-sin%28a%29sin%28b%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%28a%2Bb%29=%28-3%2F5%29%28-sqrt%285%29%2F5%29%29-%284%2F5%29%28-%282sqrt%285%29%29%2F5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%2Bb%29=%283sqrt%285%29%29%2F25%2B%288sqrt%285%29%29%2F25%29 ALIGN=MIDDLE  ALT=\"cos%28a%2Bb%29=%283sqrt%285%29%29%2F25%2B%288sqrt%285%29%29%2F25%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%28a%2Bb%29=%2811sqrt%285%29%29%2F25 ALIGN=MIDDLE  ALT=\"cos%28a%2Bb%29=%2811sqrt%285%29%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "As a check using inverse trig functions,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=126.9 ALIGN=MIDDLE  ALT=\"a=126.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=243.4 ALIGN=MIDDLE  ALT=\"b=243.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=370.3 ALIGN=MIDDLE  ALT=\"a%2Bb=370.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28370.3%29=0.9839 ALIGN=MIDDLE  ALT=\"cos%28370.3%29=0.9839\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2Asqrt%285%29%2F25=0.9839 ALIGN=MIDDLE  ALT=\"11%2Asqrt%285%29%2F25=0.9839\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );