document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158677>Question 1158677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact values of sin 2θ, cos 2θ, and tan 2θ for the given value of θ.<BR>\n" );
document.write( "cos θ = 3/5;    0° < θ < 90°\r<BR>\n" );
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document.write( "a).sin 2θ<BR>\n" );
document.write( "b).cos 2θ<BR>\n" );
document.write( "c).tan 2θ\r<BR>\n" );
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document.write( "Please help! I want to know how to solve these kind of problems so please don't just show me the answer. Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781646 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you google \"double angle formulas\", you can find<BR>\n" );
document.write( "the cos, sin, and tan of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2theta+ ALIGN=MIDDLE  ALT=\"+2theta+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+theta+%29+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+cos%28+theta+%29+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%3C+theta+%3C+90+ ALIGN=MIDDLE  ALT=\"+0+%3C+theta+%3C+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This means the angle is in the 1st quadrant where the<BR>\n" );
document.write( "cos, sin, and tan are all positive (+) / (+)<BR>\n" );
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document.write( "(a) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+2%2Atheta+%29+=+2%2Asin%28+theta+%29%2Acos%28+theta+%29+ ALIGN=MIDDLE  ALT=\"+sin%28+2%2Atheta+%29+=+2%2Asin%28+theta+%29%2Acos%28+theta+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( look it up online )<BR>\n" );
document.write( "Note that if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+theta+%29+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+cos%28+theta+%29+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have a 3-4-5 triangle, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+theta+%29+=+4%2F5+ ALIGN=MIDDLE  ALT=\"+sin%28+theta+%29+=+4%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+theta+%29+=+4%2F3+ ALIGN=MIDDLE  ALT=\"+tan%28+theta+%29+=+4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+2%2Atheta+%29+=+2%2Asin%28+theta+%29%2Acos%28+theta+%29+ ALIGN=MIDDLE  ALT=\"+sin%28+2%2Atheta+%29+=+2%2Asin%28+theta+%29%2Acos%28+theta+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+2%2Atheta+%29+=+2%2A%28+4%2F5+%29%2A%28+3%2F5+%29+ ALIGN=MIDDLE  ALT=\"+sin%28+2%2Atheta+%29+=+2%2A%28+4%2F5+%29%2A%28+3%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( all positive in the 1st quadrant )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28+2%2Atheta+%29+=+24%2F25+ ALIGN=MIDDLE  ALT=\"+sin%28+2%2Atheta+%29+=+24%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "(b) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+2%2Atheta+%29+=+2%2Acos%5E2%28+theta+%29+-+1+ ALIGN=MIDDLE  ALT=\"+cos%28+2%2Atheta+%29+=+2%2Acos%5E2%28+theta+%29+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( online )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+2%2Atheta+%29+=+2%2A%28+3%2F5+%29%5E2+-+1+ ALIGN=MIDDLE  ALT=\"+cos%28+2%2Atheta+%29+=+2%2A%28+3%2F5+%29%5E2+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+2%2Atheta+%29+=+18%2F25+-+1+ ALIGN=MIDDLE  ALT=\"+cos%28+2%2Atheta+%29+=+18%2F25+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+2%2Atheta+%29+=+-7%2F25+ ALIGN=MIDDLE  ALT=\"+cos%28+2%2Atheta+%29+=+-7%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The negative sign tells me that <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;\" > ends up in the<BR>\n" );
document.write( "2nd quadrant where the cosine is negative.<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(c) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+%28+2%2Atan%28+theta+%29%29+%2F+%28+1+-+tan%5E2%28+theta+%29+%29+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+%28+2%2Atan%28+theta+%29%29+%2F+%28+1+-+tan%5E2%28+theta+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( online )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+%28+2%2A%28+4%2F3+%29%29+%2F+%28+1+-+%28+16%2F9+%29%29+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+%28+2%2A%28+4%2F3+%29%29+%2F+%28+1+-+%28+16%2F9+%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+%28+8%2F3+%29+%2F+%28+-7%2F9+%29+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+%28+8%2F3+%29+%2F+%28+-7%2F9+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+%28+8%2F3+%29%2A%28+-9%2F7+%29+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+%28+8%2F3+%29%2A%28+-9%2F7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+-24%2F7+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+-24%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's negative because the tan is negative in the 2nd quadrant<BR>\n" );
document.write( "Notice also that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+2%2Atheta+%29+=+sin%28+2%2Atheta+%29+%2F+cos%28+2%2Atheta+%29+ ALIGN=MIDDLE  ALT=\"+tan%28+2%2Atheta+%29+=+sin%28+2%2Atheta+%29+%2F+cos%28+2%2Atheta+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-24%2F7+=+%28+24%2F25+%29+%2F+%28+-7%2F25+%29+ ALIGN=MIDDLE  ALT=\"+-24%2F7+=+%28+24%2F25+%29+%2F+%28+-7%2F25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-24%2F27+=+-24%2F7+ ALIGN=MIDDLE  ALT=\"+-24%2F27+=+-24%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Also notice that I never had to find out what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+ ALIGN=MIDDLE  ALT=\"+theta+\"   DISABLED_style= \"max-width:90%; height:auto;\" > was to<BR>\n" );
document.write( "solve these. But from the results, I know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+ ALIGN=MIDDLE  ALT=\"+theta+\"   DISABLED_style= \"max-width:90%; height:auto;\" > MUST be<BR>\n" );
document.write( "greater than 45 degrees, in order for <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;\" > to end up <BR>\n" );
document.write( "in the 2nd quadrant. I'll show this using my calculator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28+theta+%29+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+cos%28+theta+%29+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+arc+cos%28+3%2F5+%29+ ALIGN=MIDDLE  ALT=\"+theta+=+arc+cos%28+3%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+theta+=+53.13+ ALIGN=MIDDLE  ALT=\"+theta+=+53.13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Atheta++=+106.26+ ALIGN=MIDDLE  ALT=\"+2%2Atheta++=+106.26+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is in the 2nd quadrant<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Hope all this helps\r<BR>\n" );
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document.write( " </SPAN>\n" );
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