document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966917>Question 966917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a similar question to one that has been answered.\r<BR>\n" );
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document.write( "The vertical displacement of the end of a robot arm (in cm) at time t (in seconds) is given by y = 8+7cos3t + 7cos6t<BR>\n" );
document.write( "1. Find all times, t>0 (fractions of pi) where the vertical displacement is 8cm.\r<BR>\n" );
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document.write( "2. What is the first time t>0 that the vertical diplacement is 8cm?\r<BR>\n" );
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document.write( "This is what I have started doing:<BR>\n" );
document.write( "Let x = 3t<BR>\n" );
document.write( "y = 8 + 7cos(x) + 7cos(2x)<BR>\n" );
document.write( "now do I divide out 7 (from cos(x) and cos(2x)) and use a trigonometric Identity cos(2x)? which gives me cos(x) + 2cos^2x-1 <BR>\n" );
document.write( "Any help in the right direction would be appreciated. Thankyou<BR>\n" );
document.write( "Chad. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590927 by </B><A HREF=/tutors/aboutme.mpl?userid=Murthy><B>Murthy(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Murthy><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=590927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given,  y = 8+7cos3t + 7cos6t\r<BR>\n" );
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document.write( "when y=8 cm\r<BR>\n" );
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document.write( "8=8+7cos3t + 7cos6t\r<BR>\n" );
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document.write( "can be rearranged as \r<BR>\n" );
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document.write( "7(cos3t+cos6t)=0\r<BR>\n" );
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document.write( "or cos3t+cos6t =0 \r<BR>\n" );
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document.write( "2cos(9t/2).cos (3t/2)=0              {cosA + cosB = 2 cos(A+B/2).cos(A-B/2)}\r<BR>\n" );
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document.write( "or cos(9t/2).cos (3t/2)=0\r<BR>\n" );
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document.write( "This means either cos(9t/2)=0 or cos (3t/2)=0\r<BR>\n" );
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document.write( "if cos(9t/2)=0\r<BR>\n" );
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document.write( "9t/2= n(pi)/2\r<BR>\n" );
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document.write( "t=n(pi)/9\r<BR>\n" );
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document.write( "if cos (3t/2)=0\r<BR>\n" );
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document.write( "3t/2= n(pi)/2\r<BR>\n" );
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document.write( "t=n(pi)/3\r<BR>\n" );
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document.write( "The first time when displacement is 8 cm is t=pi/9 </SPAN>\n" );
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