document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204615>Question 1204615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that <BR>\n" );
document.write( "sin(a) = <BR>\n" );
document.write( "4<BR>\n" );
document.write( "5<BR>\n" );
document.write( " and <BR>\n" );
document.write( "cos(b) = − <BR>\n" );
document.write( "1<BR>\n" );
document.write( "3<BR>\n" );
document.write( ",<BR>\n" );
document.write( " with a and b both in the interval \r<BR>\n" );
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document.write( "𝜋<BR>\n" );
document.write( "2<BR>\n" );
document.write( ", 𝜋\r<BR>\n" );
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document.write( ",<BR>\n" );
document.write( " find the exact values of <BR>\n" );
document.write( "sin(a + b)<BR>\n" );
document.write( " and<BR>\n" );
document.write( "cos(a − b).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840969 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Question: Given that sin(a) = 4/5 and cos(b) = -1/3, with a and b both in the interval [pi/2, pi], find the exact values of<BR>\n" );
document.write( "sin(a+b)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "cos(a-b)\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "The pythagorean trig identity is useful here. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2Bcos%5E2%28x%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2Bcos%5E2%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use that identity to go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%29+=+4%2F5 ALIGN=MIDDLE  ALT=\"sin%28a%29+=+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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( "Angle 'a' is in quadrant 2 where cosine is negative.<BR>\n" );
document.write( "I'll leave the steps and scratch work for the student to do.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28b%29+=+-1%2F3 ALIGN=MIDDLE  ALT=\"cos%28b%29+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28b%29+=+%282%2Asqrt%282%29%29%2F3 ALIGN=MIDDLE  ALT=\"sin%28b%29+=+%282%2Asqrt%282%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > due to the pythagorean trig identity. <BR>\n" );
document.write( "Sine is positive in quadrant Q2.\r<BR>\n" );
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document.write( "We'll then turn to this identity<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2Bb%29+=+sin%28a%29cos%28b%29%2Bcos%28a%29sin%28b%29 ALIGN=MIDDLE  ALT=\"sin%28a%2Bb%29+=+sin%28a%29cos%28b%29%2Bcos%28a%29sin%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which leads to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2Bb%29+=+%284%2F5%29%28-1%2F3%29%2B%28-3%2F5%29%2A%28%282%2Asqrt%282%29%29%2F3%29 ALIGN=MIDDLE  ALT=\"sin%28a%2Bb%29+=+%284%2F5%29%28-1%2F3%29%2B%28-3%2F5%29%2A%28%282%2Asqrt%282%29%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2Bb%29+=+%28-4-6%2Asqrt%282%29%29%2F15 ALIGN=MIDDLE  ALT=\"sin%28a%2Bb%29+=+%28-4-6%2Asqrt%282%29%29%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "And,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a-b%29+=+cos%28a%29cos%28b%29%2Bsin%28a%29sin%28b%29 ALIGN=MIDDLE  ALT=\"cos%28a-b%29+=+cos%28a%29cos%28b%29%2Bsin%28a%29sin%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a-b%29+=+%28-3%2F5%29%2A%28-1%2F3%29%2B%284%2F5%29%2A%28%282%2Asqrt%282%29%29%2F3%29 ALIGN=MIDDLE  ALT=\"cos%28a-b%29+=+%28-3%2F5%29%2A%28-1%2F3%29%2B%284%2F5%29%2A%28%282%2Asqrt%282%29%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a-b%29+=+%283%2B8%2Asqrt%282%29%29%2F15 ALIGN=MIDDLE  ALT=\"cos%28a-b%29+=+%283%2B8%2Asqrt%282%29%29%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "</font> </SPAN>\n" );
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