document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628586>Question 628586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me evaluate this function. \r<BR>\n" );
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document.write( "tan((B)beta-(a)alpha) if sin(a)=4/5 and cos(B)=-12/13 <BR>\n" );
document.write( "(alpha in first quadrant) and (beta in second quadrant) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396303 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=396303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help me evaluate this function. <BR>\n" );
document.write( "tan((B)beta-(a)alpha) if sin(a)=4/5 and cos(B)=-12/13 <BR>\n" );
document.write( "(alpha in first quadrant) and (beta in second quadrant<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Trig Identity:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29 ALIGN=MIDDLE  ALT=\"tan%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "cosB=-12/13=adjacent side/hypotenuse<BR>\n" );
document.write( "opposite side=&#8730;(13^2-12^2)=&#8730;(25)=5<BR>\n" );
document.write( "tanB=-5/12 in quadrant II where tan<0 (opposite side/adjacent side)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sinA=4/5=opposite side/hypotenuse<BR>\n" );
document.write( "adjacent side=3 (3-4-5 right triangle)<BR>\n" );
document.write( "tanA=4/3 in quadrant I where tan>0 (opposite side/adjacent side)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29 ALIGN=MIDDLE  ALT=\"tan%28B-A%29=%28tanB-tanA%29%2F%281%2BtanA%2AtanB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28B-A%29=%28-5%2F12-4%2F3%29%2F%281%2B4%2F3%2A-5%2F12%29 ALIGN=MIDDLE  ALT=\"tan%28B-A%29=%28-5%2F12-4%2F3%29%2F%281%2B4%2F3%2A-5%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28B-A%29=%28-5%2F12-16%2F12%29%2F%281-20%2F36%29 ALIGN=MIDDLE  ALT=\"tan%28B-A%29=%28-5%2F12-16%2F12%29%2F%281-20%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28B-A%29=%28-21%2F12%29%2F%2816%2F36%29 ALIGN=MIDDLE  ALT=\"tan%28B-A%29=%28-21%2F12%29%2F%2816%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "tan(B-A)&#8776;-3.94<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "sinA=4/5<BR>\n" );
document.write( "A=53.13º<BR>\n" );
document.write( "cosB=-12/13<BR>\n" );
document.write( "B=157.38º<BR>\n" );
document.write( "B-A=157.38-53.13=104.25<BR>\n" );
document.write( "tan(B-A)=tan(104.25º)&#8776;3.9375<BR>\n" );
document.write( " </SPAN>\n" );
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