document.write( "Question 1143227: What is the minimum value of cos(theta) + 2cos(theta +240) \n" ); document.write( "
Algebra.Com's Answer #764045 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "\"+y+=+cos%28t%29+%2B+2cos%28t%2B240%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"+dy%2Fdt+=+-sin%28t%29+-+2sin%28t%2B240%29+\"\r
\n" ); document.write( "\n" ); document.write( "Set dy/dt = 0 to find critical points:\r
\n" ); document.write( "\n" ); document.write( "\"+dy%2Fdt+=+-sin%28t%29+-+2sin%28t%2B240%29+=+0+\" \r
\n" ); document.write( "\n" ); document.write( "dy/dt is zero at t = -90 degrees (and every +/- 180 degrees added to that)\r
\n" ); document.write( "\n" ); document.write( "zeros are at t = \"+n%2A180+-+90+\" degrees \r
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\n" ); document.write( "\n" ); document.write( " n t (deg) y
\n" ); document.write( "--- ------- ---
\n" ); document.write( " -1 -270 \"+sqrt%283%29+\"
\n" ); document.write( " 0 -90 \"+-sqrt%283%29+\"
\n" ); document.write( " 1 90 \"+sqrt%283%29+\"
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\n" ); document.write( "The minimum value is \"+highlight%28-sqrt%283%29%29+\" (approx. -1.732051) at t=-90 degrees
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