document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180061>Question 180061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine exact values.<BR>\n" );
document.write( "Find sin A and cos A if tan A=5/3 and cos A <0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854681 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53937)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Trigonometry-basics/180061: Determine exact values.<BR>\n" );
document.write( "Find sin(A) and cos(A) if tan(A) = 5/3 and cos(A) < 0.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculations in the post by @HyperBrain are incorrect, producing wrong answer.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For correct solution, see my post below.\r<BR>\n" );
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document.write( "Let A be an angle, sin(A) = a/c, cos(A) = b/c, tan(A) = a/b. Where<BR>\n" );
document.write( "a=opposite side<BR>\n" );
document.write( "b=adjacent side<BR>\n" );
document.write( "c=hypotenuse\r<BR>\n" );
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document.write( "a, b, and c form a right triangle and therefore must satisfy,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since tan(A) is positive and cos(A) is negative (given),<BR>\n" );
document.write( "we conclude from it that A is in QIII.\r<BR>\n" );
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document.write( "Since tan(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, let a = -5, b = -3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"5%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 25+9 = 34,<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2834%29 ALIGN=MIDDLE  ALT=\"sqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "sin(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Fsqrt%2834%29 ALIGN=MIDDLE  ALT=\"-5%2Fsqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%285sqrt%2834%29%29%2F34 ALIGN=MIDDLE  ALT=\"-%285sqrt%2834%29%29%2F34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cos(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Fsqrt%2834%29 ALIGN=MIDDLE  ALT=\"-3%2Fsqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283sqrt%2834%29%29%2F34 ALIGN=MIDDLE  ALT=\"-%283sqrt%2834%29%29%2F34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solved correctly.\r<BR>\n" );
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