document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73914>Question 73914</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If (theta) is a second-quadrant with cos(theta)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fsqrt5 ALIGN=MIDDLE  ALT=\"2%2Fsqrt5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the exact value of cos2(theta).\r<BR>\n" );
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document.write( "a. -3/5<BR>\n" );
document.write( "b. -2/5<BR>\n" );
document.write( "c. 2/5<BR>\n" );
document.write( "d. 3/5<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 #52928 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=52928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If (theta) is a second-quadrant with cos(theta)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Fsqrt5 ALIGN=MIDDLE  ALT=\"-2%2Fsqrt5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the exact value of cos2(theta).<BR>\n" );
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document.write( "cos(2theta)= cos^2(theta) - sin^2(theta)<BR>\n" );
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document.write( "Need to find sin(theta)<BR>\n" );
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document.write( "cos(theta) = adj/hyp = 2/sqrt5<BR>\n" );
document.write( "adjacent is an x-value; it is negative in the 2nd quadrant;<BR>\n" );
document.write( "therefore the cos(theta) is negative; it must be -2/sqrt5<BR>\n" );
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document.write( "If adj = -2  and hyp = sqrt5 then opp = sqrt((sqrt5)^2-2^2))= 1<BR>\n" );
document.write( "Therefore sin(theta)= opp/hyp = 1/2sqrt5<BR>\n" );
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document.write( "Then cos(2theta)= (2/sqrt5)^2 - (1/sqrt5)^2 = 3/5 <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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