document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=593699>Question 593699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the amplitude, period, phase shift, and vertical shift for Y=2 cos 1/2( theta + pi/2 ) -2 Then graph the function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376554 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=376554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> State the amplitude, period, phase shift, and vertical shift for Y=2 cos 1/2( theta + pi/2 ) -2 Then graph the function.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Use x for theta<BR>\n" );
document.write( "Equation for graphing cos functions: y=Acos(Bx-C), A=amplitude,Period=2&#960;/B, Phase shift=C/B<BR>\n" );
document.write( "For given equation: <BR>\n" );
document.write( "2cos(1/2)(x+&#960;/2)-2:<BR>\n" );
document.write( "re-write equation:<BR>\n" );
document.write( "2cos(x/2+&#960;/4)-2<BR>\n" );
document.write( "Amplitude=2<BR>\n" );
document.write( "B=1/2<BR>\n" );
document.write( "period=2&#960;/B=2&#960;/(1/2)=4&#960;<BR>\n" );
document.write( "1/4 period=&#960;<BR>\n" );
document.write( "C=&#960;/4<BR>\n" );
document.write( "phase shift=C/B=(&#960;/4)/(1/2)=&#960;/2 (to the left)<BR>\n" );
document.write( "curve is bumped down 2 units.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Drawing a graph for one period with x-axis scale in radians:<BR>\n" );
document.write( "With no phase-shift, coordinates of given cos function are as follows:<BR>\n" );
document.write( "(0,2), (&#960;,0), (2&#960;,-2), (3&#960;,0), (4&#960;,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "With phase-shift to the left, x-coordinates are changed as follows:<BR>\n" );
document.write( "(-&#960;/2,2), (&#960;/2,0), (3&#960;/2,-2), (5&#960;/2,0), (7&#960;/2,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "With bumping of 2 units down, y-coordinates are changed as follows:<BR>\n" );
document.write( "(-&#960;/2,0), (&#960;/2,-2), (3&#960;/2,-4), (5&#960;/2,-2), (7&#960;/2,0)<BR>\n" );
document.write( "These are coordinates of the final curve you can graph.\r<BR>\n" );
document.write( "\n" );
document.write( "One more item to calculate:<BR>\n" );
document.write( "y-intercept<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "2cos(x/2+&#960;/4)-2<BR>\n" );
document.write( "2cos(&#960;/4)-2<BR>\n" );
document.write( "2*&#8730;2/2-2=&#8730;2-2&#8776;-.59\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );