document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750083>Question 750083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> state the amplitude, period, phase shift, and vertical shift for the function. Then graph the function. y=4cos[3theta+(3/2)pi]+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456440 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=456440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> state the amplitude, period, phase shift, and vertical shift for the function. Then graph the function. y=4cos[3theta+(3/2)pi]+2<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Equation for cos function: y=Acos(Bx-C), A=amplitude, period=2&#960;/B, phase shift=C/B<BR>\n" );
document.write( "For given equation: y=4cos(3x+3&#960;/2)+2<BR>\n" );
document.write( "A=4<BR>\n" );
document.write( "B=3<BR>\n" );
document.write( "period=2&#960;/B=2&#960;/3<BR>\n" );
document.write( "1/4 period=2&#960;/12=&#960;/6<BR>\n" );
document.write( "C=3&#960;/2<BR>\n" );
document.write( "phase shift=C/B=(3&#960;/2)/3=&#960;/2 (shift to the left)=3&#960;/6<BR>\n" );
document.write( "curve is bumped up 2 units<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Graphing function:<BR>\n" );
document.write( "On an x-y coordinate system with the x-axis scaled in radians, start with coordinates of the basic cos functon with period=2&#960;/3,amplitude =1, phase shift=0, vertical shift=0, for one period.<BR>\n" );
document.write( "coordinates of basic cos function:<BR>\n" );
document.write( "(0,1), (&#960;/6,0), (&#960;/3,-1), (&#960;/2,0), (2&#960;/3,1), (5&#960;/6,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "shift curve &#960;/2 to the left:<BR>\n" );
document.write( "(-&#960;/2,1), (-&#960;/3,0), (-&#960;/6,-1), (0,0), (&#960;/6,1), (&#960;/3,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "change amplitude to 4:<BR>\n" );
document.write( "(-&#960;/2,4), (-&#960;/3,0), (-&#960;/6,-4), (0,0), (&#960;/6,4), (&#960;/3,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "vertical shift up 2 units (final configuration)<BR>\n" );
document.write( "(-&#960;/2,6), (-&#960;/3,2), (-&#960;/6,-2), (0,2), (&#960;/6,6), (&#960;/3,2)\r<BR>\n" );
document.write( "\n" );
document.write( "set x=0<BR>\n" );
document.write( "y-intercept: 4cos(3x+3&#960;/2)+2=4cos(3&#960;/2)+2=-4+2=2<BR>\n" );
document.write( "              <BR>\n" );
document.write( "..<BR>\n" );
document.write( "It is easy to make a mistake here. Please check my calculations. </SPAN>\n" );
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