document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199044>Question 1199044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If tan 𝛼 = − 12/35 and cot 𝛽 = 3/4<BR>\n" );
document.write( " for a second-quadrant angle 𝛼 and a third-quadrant angle 𝛽, find the following.<BR>\n" );
document.write( "(a)    sin(𝛼 + 𝛽) <BR>\n" );
document.write( "(c)    tan(𝛼 + 𝛽) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832777 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20855)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28alpha%29+=+-12%2F35 ALIGN=MIDDLE  ALT=\"tan+%28alpha%29+=+-12%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28beta%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"cot+%28beta%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for a second-quadrant angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a third-quadrant angle  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta ALIGN=MIDDLE  ALT=\"beta\"   DISABLED_style= \"max-width:90%; height:auto;\" > , find the following:\r<BR>\n" );
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document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28alpha+%2B+beta%29 ALIGN=MIDDLE  ALT=\"sin%28alpha+%2B+beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28alpha+%2B+beta%29%7D%7D%5D%0D%0A%0D%0A%0D%0A%7B%7B%7Btan+%28alpha%29+=+-12%2F35+=opp%2Fadj ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=12 ALIGN=MIDDLE  ALT=\"opp=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=adj=35 ALIGN=MIDDLE  ALT=\"adj=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hyp=sqrt%2812%5E2%2B35%5E2%29=37+ ALIGN=MIDDLE  ALT=\"hyp=sqrt%2812%5E2%2B35%5E2%29=37+\"   DISABLED_style= \"max-width:90%; height:auto;\" >or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37 ALIGN=MIDDLE  ALT=\"-37\"   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%28alpha%29=12%2F37 ALIGN=MIDDLE  ALT=\"sin%28alpha%29=12%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28alpha%29=-12%2F37 ALIGN=MIDDLE  ALT=\"sin%28alpha%29=-12%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "for a second-quadrant angle  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28alpha%29=12%2F37 ALIGN=MIDDLE  ALT=\"sin%28alpha%29=12%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot+%28beta%29+=+3%2F4=adj%2Fopp ALIGN=MIDDLE  ALT=\"cot+%28beta%29+=+3%2F4=adj%2Fopp\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=adj=3 ALIGN=MIDDLE  ALT=\"adj=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=4 ALIGN=MIDDLE  ALT=\"opp=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hyp=sqrt%284%5E2%2B3%5E2%29=sqrt%2825%29=5 ALIGN=MIDDLE  ALT=\"hyp=sqrt%284%5E2%2B3%5E2%29=sqrt%2825%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5 ALIGN=MIDDLE  ALT=\"+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=+3%2F5 ALIGN=MIDDLE  ALT=\"cos%28beta%29=+3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a third-quadrant angle  (beta): \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=-3%2F5 ALIGN=MIDDLE  ALT=\"cos%28beta%29=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, use<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28alpha%29=12%2F37 ALIGN=MIDDLE  ALT=\"sin%28alpha%29=12%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28beta%29=-3%2F5 ALIGN=MIDDLE  ALT=\"cos%28beta%29=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28alpha+%2B+beta%29=cos%28-3%2F5%29+sin%2812%2F37%29+%2B+cos%2812%2F37%29+sin%28-3%2F5%29=-0.2721971 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(c)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28alpha+%2B+beta%29=+sin%28alpha+%2B+beta%29%2Fcos%28alpha+%2B+beta%29 ALIGN=MIDDLE  ALT=\"+tan%28alpha+%2B+beta%29=+sin%28alpha+%2B+beta%29%2Fcos%28alpha+%2B+beta%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=-0.2721971%2F%28cos%2812%2F37%29+cos%28-3%2F5%29+-+sin%2812%2F37%29+sin%28-3%2F5%29%29 ALIGN=MIDDLE  ALT=\"-0.2721971%2F%28cos%2812%2F37%29+cos%28-3%2F5%29+-+sin%2812%2F37%29+sin%28-3%2F5%29%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=-0.2721971%2F0.9622415002904475 ALIGN=MIDDLE  ALT=\"-0.2721971%2F0.9622415002904475\"   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=-0.2828782 ALIGN=MIDDLE  ALT=\"-0.2828782\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );