document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867967>Question 867967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin&#952;=3/8 and &#952; is in the first quadrant, what is sin2&#952;. Include a diagram\r<BR>\n" );
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document.write( "Please help as my friends and I have been stumped on this one. I know that for the diagram, the missing side is simply:\r<BR>\n" );
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document.write( "8^2-3^2=x^2<BR>\n" );
document.write( "64-9= x^2<BR>\n" );
document.write( "55= x^2<BR>\n" );
document.write( "Sqrt55=x<BR>\n" );
document.write( "7.4162=x\r<BR>\n" );
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document.write( "We've also tried using double angle Identity and got as far as:\r<BR>\n" );
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document.write( "      sin(2x)=2(3/8)cosx<BR>\n" );
document.write( "sin(2x)=2(3/8)(7.1462/8)<BR>\n" );
document.write( "sin(2x)=2(3)(7.1562)/64<BR>\n" );
document.write( " before realizing we might be wrong. \r<BR>\n" );
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document.write( "Also please help with the diagramming as well if you can, since we're also trying to figure out if the numbers from sin&#952; double in it. (i.e. hypotenuse times 2, etc)\r<BR>\n" );
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document.write( "Thanks!<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 #523278 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=523278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identity, double angle:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sine%282%2Atheta%29=2%2Asin%28theta%29cos%28theta%29 ALIGN=MIDDLE  ALT=\"sine%282%2Atheta%29=2%2Asin%28theta%29cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use also the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which gives you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=sqrt%281-sin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29=sqrt%281-sin%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "sine is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you want as the double angle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282%2Atheta%29=2%283%2F8%29%2Acos%28theta%29 ALIGN=MIDDLE  ALT=\"sin%282%2Atheta%29=2%283%2F8%29%2Acos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sin%282%2Atheta%29=2%283%2F8%29%2Asqrt%281-%283%2F8%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28sin%282%2Atheta%29=2%283%2F8%29%2Asqrt%281-%283%2F8%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----only needing computation to finish into final value simplified.\r<BR>\n" );
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document.write( "Decimal approximation, 0.695, but I suggest working through into simplest radical form, FIRST.\r<BR>\n" );
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document.write( "Note that for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=3%2F8 ALIGN=MIDDLE  ALT=\"sin%28theta%29=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is an angle of about 22 degrees.   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Atheta ALIGN=MIDDLE  ALT=\"2%2Atheta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is still in the first quadrant.   </SPAN>\n" );
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