document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251050>Question 251050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Heres 3 questions I was curious about\r<BR>\n" );
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document.write( "Given sin A = 1/3 A in Quad II, CosB = -3/5 B in Quad III,\r<BR>\n" );
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document.write( "find Sin(A+B) and tan2B\r<BR>\n" );
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document.write( "Solve for x : 0 < or = x < or = 360\r<BR>\n" );
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document.write( "3cos^2x = cosx    AND 3cos^2x - 5sinx = 1\r<BR>\n" );
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document.write( "prove this identity:\r<BR>\n" );
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document.write( "sin2x/sinx - cos2x/cosx = secx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184606 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets take them one at a time:<BR>\n" );
document.write( "Given sin A = 1/3 A in Quad II, CosB = -3/5 B in Quad III, <BR>\n" );
document.write( "find Sin(A+B) and tan2B \r<BR>\n" );
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document.write( "Sin A = 1/3, Cos A = -2*sqrt(2)/3<BR>\n" );
document.write( "Sin B = -4/5 Cos B = -3/5<BR>\n" );
document.write( "Sin(A+B) = SinACosB + CosASinB = (1/3)(-3/5) + (2*sqrt(2)/3)(-4/5) = -3/15 - 8*sqrt(2)/15.<BR>\n" );
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document.write( "Solve for x : 0 < or = x < or = 360 <BR>\n" );
document.write( "3cos^2x = cosx AND 3cos^2x - 5sinx = 1 \r<BR>\n" );
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document.write( "3cos^2(x) - cos(x) = 0<BR>\n" );
document.write( "cos(x) [3cos(x) - 1] = 0<BR>\n" );
document.write( "cos(x) = 0 - -> X = pi/2 or 3pi/2<BR>\n" );
document.write( "3cos(x) - 1 = 0 <BR>\n" );
document.write( "cos(x) = 1/3 - -> ~ 70.5 degrees\r<BR>\n" );
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document.write( "3cos^2(x) - 5Sin(x) = 1<BR>\n" );
document.write( "we use an identity: sin^2x + cos^2x = 1.<BR>\n" );
document.write( "3[1 - sin^2(x)]  - 5sin(x) = 1<BR>\n" );
document.write( "3Sin^2(x) + 5sin(x) -2 = 0<BR>\n" );
document.write( "(3Sin(x) - 1)(Sin(x) + 2) = 0<BR>\n" );
document.write( "3sin(x) - 1 = 0<BR>\n" );
document.write( "sin(x) = 1/3 - -> ~19.5 degrees<BR>\n" );
document.write( "sin(x) - 2 = 0 - - > no solution.\r<BR>\n" );
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document.write( "\"AND\" needs over lap, there is none here. However if you used substitution and set cos(x) = 5sin(x) + 1. The only values that work are 0 degrees and 360 degrees.\r<BR>\n" );
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document.write( "prove this identity: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin2x%2Fsinx+-+cos2x%2Fcosx+=+secx ALIGN=MIDDLE  ALT=\"sin2x%2Fsinx+-+cos2x%2Fcosx+=+secx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First we want to turn the more complicated side into the less complicated side. I will start with the left side.<BR>\n" );
document.write( "An identity we need is: sin2x = 2sinxcosx<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sinxcosx%2Fsinx+-+cos2x%2Fcosx ALIGN=MIDDLE  ALT=\"2sinxcosx%2Fsinx+-+cos2x%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cosx+-+cos2x%2Fcosx ALIGN=MIDDLE  ALT=\"2cosx+-+cos2x%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "2cos^2x - cos2x / cosx<BR>\n" );
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document.write( "Another identity we need is: cos2x = cos^2x - sin^2x = 2cos^2x - 1<BR>\n" );
document.write( "2cos^2x - (2cos^2x - 1 / cosx<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcosx ALIGN=MIDDLE  ALT=\"1%2Fcosx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "sec(x) </SPAN>\n" );
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