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 #52931 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem has an error in it.  It tells you that theta is in the second quadrant,<BR>\n" );
document.write( "but it gives you a positive value for the cosine of theta.  You need to recognize that in<BR>\n" );
document.write( "the second quadrant the cosine is negative.  Cosine is only positive in quadrants I and IV.<BR>\n" );
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document.write( "Here's a way to do the problem quickly using a scientific calculator ($10 type).<BR>\n" );
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document.write( "Set you calculator into the degrees mode.  Divide 2 by the square root of 5 and use the<BR>\n" );
document.write( "change sign mode to make the answer a negative number.  Your answer should be -0.894427191.<BR>\n" );
document.write( "This is the decimal value of the cosine of theta.<BR>\n" );
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document.write( "Next use the arccosine function (cos^-1 function which is normally shift+cos keys) and you <BR>\n" );
document.write( "should find that the angle whose cosine is -0.894427191 is 153.4349488 degrees.  Multiply this <BR>\n" );
document.write( "angle by 2 to get two theta. You should have 306.8698976 degrees for 2 theta. (Note that <BR>\n" );
document.write( "this angle is in quadrant IV where the cosine is positive.)  Now that you have found 2 theta, <BR>\n" );
document.write( "just press the cosine key and you should find that the cosine of 2 theta is 0.6 which is the <BR>\n" );
document.write( "same as +3/5.<BR>\n" );
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document.write( "Answer d is the correct answer.  <BR>\n" );
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document.write( "Hope this helps. Using a calculator makes it go fast. </SPAN>\n" );
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