document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526717>Question 526717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if cos theta = -2/3 and 450 degrees < theta < 540degrees, find\r<BR>\n" );
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document.write( "a. the exact value of cos (1/2) theta<BR>\n" );
document.write( "b. the exact value of tan 2theta </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #348681 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=348681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if cos theta = -2/3 and 450 degrees < theta < 540degrees, find <BR>\n" );
document.write( "a. the exact value of cos (1/2) theta<BR>\n" );
document.write( "b. the exact value of tan 2theta  <BR>\n" );
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document.write( "using x in place of theta<BR>\n" );
document.write( "450º < x < 540º places the angle in quadrant II where cos<0<BR>\n" );
document.write( "cos x=-2/3 means you are working with a right triangle whose adjacent side is= -2, and the hypotenuse=3. By the Pythagorean Theorem, the opposite side=&#8730;5. <BR>\n" );
document.write( "Angle x=arccos(-2/3)+360º=131.81º+360=491.81º<BR>\n" );
document.write( "Reference angle=540-491.81=48.19º<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a. cos x/2=±&#8730;[(1+cosx)/2]=-&#8730;[(1-2/3)/2]=-&#8730;(1/6)=-1/&#8730;6=-&#8730;6/6=-0.408..<BR>\n" );
document.write( "check: cos(x/2)=cos(491.81/2)=cos(245.91º)=-0.408..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b. tan2x=(2 tanx)/(1-tan^2x)<BR>\n" );
document.write( "tan x=&#8730;5/-2 (opposite side/adjacent side)<BR>\n" );
document.write( "tan^2x=5/4<BR>\n" );
document.write( "tan2x==2*(&#8730;5/-2)/(1-5/4)=-&#8730;5/(-1/4)=4&#8730;5=8.94..<BR>\n" );
document.write( "tan 2x=tan(2*491.81)=tan(983.62º)=8.94..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "a. exact value of cos (1/2) theta=-&#8730;6/6<BR>\n" );
document.write( "b. exact value of tan 2theta =4&#8730;5 </SPAN>\n" );
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