document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198569>Question 198569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos&#952;=0.8 and 270<&#952; <360, find the exact value of sin2&#952; <BR>\n" );
document.write( "a. -0.96<BR>\n" );
document.write( "b. -0.6<BR>\n" );
document.write( "c. 0.96<BR>\n" );
document.write( "d. 0.28\r<BR>\n" );
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document.write( "Is it A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149091 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=149091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta)+\cos^2(\theta)=1\">\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos(\theta)=0.8\">, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2(\theta)=0.8^2=0.64\">. Plug this into the identity above to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta)+0.64=1\">\r<BR>\n" );
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document.write( "Now solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta)\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2(\theta)=1-0.64=0.36\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(\theta)=\sqrt{0.36}=0.6\">\r<BR>\n" );
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document.write( "Now because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 270< \theta < 360\">, this means that the value of sine will be negative. \r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(\theta)=-0.6\">\r<BR>\n" );
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document.write( "Now recall the identity: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(2\theta)=2\sin(\theta)\cos(\theta)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(2\theta)=2\sin(\theta)\cos(\theta)\"> ... Start with the given identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(2\theta)=2(-0.6)(0.8)\"> ... Plug in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(\theta)=-0.6\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos(\theta)=0.8\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(2\theta)=-0.96\"> ... Multiply\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(2\theta)=-0.96\"> which means that the answer is A) -0.96. So you are correct. Good job. </SPAN>\n" );
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