document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204736>Question 1204736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <BR>\n" );
document.write( "sin(x) = <BR>\n" );
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document.write( "5<BR>\n" );
document.write( " and x is in quadrant I, find the exact values of the expressions without solving for x.<BR>\n" );
document.write( "(a)    sin(2x)<BR>\n" );
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document.write( "(b)    cos(2x)<BR>\n" );
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document.write( "(c)    tan(2x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841188 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "If<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=1%2F5 ALIGN=MIDDLE  ALT=\"sin%28x%29+=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is in quadrant I, find the exact values of the expressions without solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in quadrant I sin, cos, and tan are positive\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=1%2F5 ALIGN=MIDDLE  ALT=\"sin%28x%29+=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fc=1%2F5 ALIGN=MIDDLE  ALT=\"a%2Fc=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1+ ALIGN=MIDDLE  ALT=\"a=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using Pythagorean theorem,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%285%5E2-1%5E2%29 ALIGN=MIDDLE  ALT=\"b=sqrt%285%5E2-1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%2824%29 ALIGN=MIDDLE  ALT=\"b=sqrt%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%284%2A6%29 ALIGN=MIDDLE  ALT=\"b=sqrt%284%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"b=2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2sqrt%286%29 ALIGN=MIDDLE  ALT=\"b=-2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we need positive value\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"b=2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=%282sqrt%286%29%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28x%29=%282sqrt%286%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2cos%28x%29%2A+sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%282x%29=2cos%28x%29%2A+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2%28%282sqrt%286%29%29%2F5%29+%2A%281%2F5%29 ALIGN=MIDDLE  ALT=\"sin%282x%29=2%28%282sqrt%286%29%29%2F5%29+%2A%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=%284sqrt%286%29%29%2F25 ALIGN=MIDDLE  ALT=\"sin%282x%29=%284sqrt%286%29%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29=cos%5E2%28x%29+-+sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"cos%282x%29=cos%5E2%28x%29+-+sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29=%28%282sqrt%286%29%29%2F5%29%5E2+-+%281%2F5%29%5E2 ALIGN=MIDDLE  ALT=\"cos%282x%29=%28%282sqrt%286%29%29%2F5%29%5E2+-+%281%2F5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29=24%2F25-+1%2F25 ALIGN=MIDDLE  ALT=\"cos%282x%29=24%2F25-+1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29=23%2F25 ALIGN=MIDDLE  ALT=\"cos%282x%29=23%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(c) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282x%29=sin%282x%29%2Fcos%282x%29 ALIGN=MIDDLE  ALT=\"tan%282x%29=sin%282x%29%2Fcos%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282x%29=%28%284sqrt%286%29%29%2F25%29%2F%2823%2F25%29 ALIGN=MIDDLE  ALT=\"tan%282x%29=%28%284sqrt%286%29%29%2F25%29%2F%2823%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282x%29=%284sqrt%286%29%29%2F23 ALIGN=MIDDLE  ALT=\"tan%282x%29=%284sqrt%286%29%29%2F23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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