document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=961988>Question 961988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: If A is an acute angle such that SinA = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+sqrt%282%29%2F3 ALIGN=MIDDLE  ALT=\"2+sqrt%282%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > calculate without a calculator (1) cosA (2) sin2A  (3) Tan2A \r<BR>\n" );
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document.write( "I tried to first get the reference angle and solve it by finding a general solution but then I remembered that I can't use my calculator.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587723 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=587723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> well, you can't use a calculator to solve the problem, but you can use a calculator to see if you solved it correctly.<BR>\n" );
document.write( "they didn't say you couldn't do that.\r<BR>\n" );
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document.write( "first we'll solve without the use of the calculator.\r<BR>\n" );
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document.write( "you are given that sinA = 2*sqrt(2)/3\r<BR>\n" );
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document.write( "draw yourself a triangle and call it ABC with your angle in question at A.<BR>\n" );
document.write( "since sine is opposite / hypotenuse, then opp/hyp = 2*sqrt(2)/3.\r<BR>\n" );
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document.write( "this says that opp = 2*sqrt(3) and h = 3 because opp/hyp = 2*sqrt(3) / 3.\r<BR>\n" );
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document.write( "use the pythagorean formula to solve for adj.\r<BR>\n" );
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document.write( "you will find that adj is equal to 1.\r<BR>\n" );
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document.write( "your triangle has:\r<BR>\n" );
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document.write( "hyp = 3<BR>\n" );
document.write( "opp = 2 * sqrt(2)<BR>\n" );
document.write( "adj = 1\r<BR>\n" );
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document.write( "you get sinA = opp/hyp = 2 * sqrt(2) / 3\r<BR>\n" );
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document.write( "you get cosA = adj/hyp = 1/3\r<BR>\n" );
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document.write( "you get tanA = opp/adj = 2*sqrt(2).\r<BR>\n" );
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document.write( "you now want to find sin2A.\r<BR>\n" );
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document.write( "the formula for that is sin2A = 2*sinA*cosA\r<BR>\n" );
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document.write( "that becomes sin2A = 2*2*sqrt(2)/3*1/3 which becomes sin2A = 4*sqrt(2)/9.\r<BR>\n" );
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document.write( "you now want to find tan2A.\r<BR>\n" );
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document.write( "the formula for that is tan2A = (2*tanA) / (1-tan^2(A)).\r<BR>\n" );
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document.write( "that becomes tan2A = 2*2*sqrt(2) / (1-(2*sqrt(2))^2) which becomes:\r<BR>\n" );
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document.write( "tan2A = 4*sqrt(2) / (1 - 4*2) which becomes:\r<BR>\n" );
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document.write( "tan2A = 4*sqrt(2) / -7.\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "sinA = 2*sqrt(2)/3<BR>\n" );
document.write( "cosA = 1/3<BR>\n" );
document.write( "tanA = 2*sqrt(2)<BR>\n" );
document.write( "sin2A = 4*sqrt(2)/9<BR>\n" );
document.write( "tan2A = 4*sqrt(2)/(-7)\r<BR>\n" );
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document.write( "you can confirm using your calculator.\r<BR>\n" );
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document.write( "first find the angle and then calculate the functions and then compare those functions with what you have here.\r<BR>\n" );
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document.write( "they should match.\r<BR>\n" );
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document.write( "the calculator will give you decimal equivalents.<BR>\n" );
document.write( "just find the decimal equivalents of what you have here and you'll get your match.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "sinA = 2*sqrt(2)/3.<BR>\n" );
document.write( "solve for A to get A = 70.52877937 degrees.\r<BR>\n" );
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document.write( "tan2A = 4*sqrt(2)/(-7)\r<BR>\n" );
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document.write( "use the calculator to get tan(2*70.52877937) = tan(141.0575587) = -.8081220356\r<BR>\n" );
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document.write( "use the calculator to calculate 4*sqrt(2)/(-7) and you will find that the calculator tells you that the value is -.8081220356.\r<BR>\n" );
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document.write( "they match so the solution is good.\r<BR>\n" );
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