document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064124>Question 1064124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello.  I need to find the (1) amplitude; (2) period; and (3) phase shift without graphing for this problem:  \r<BR>\n" );
document.write( "\n" );
document.write( "y = 2 sin(2x-pi)\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you in advance.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679167 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=679167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+A%2Asin%28k%2Ax+%2B+C%29+%2B+D ALIGN=MIDDLE  ALT=\"+y+=+A%2Asin%28k%2Ax+%2B+C%29+%2B+D\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "A = amplitude<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2FT ALIGN=MIDDLE  ALT=\"2pi%2FT\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where T=period (Note also that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=2pi%2Fk+ ALIGN=MIDDLE  ALT=\"T=2pi%2Fk+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "C/k = phase shift (Note: if  C < 0, we are shifting toward the right along the x-axis)<BR>\n" );
document.write( "D = vertical shift along y-axis, (if D < 0 we are shifting up along positive y-axis)<BR>\n" );
document.write( "—<BR>\n" );
document.write( "Comparing the above to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=2sin%282x-pi%29+ ALIGN=MIDDLE  ALT=\"+y=2sin%282x-pi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   we get:\r<BR>\n" );
document.write( "\n" );
document.write( "Amplitude = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+2+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Period = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Fk+=+2pi%2F2+=+highlight%28pi%29+ ALIGN=MIDDLE  ALT=\"2pi%2Fk+=+2pi%2F2+=+highlight%28pi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Phase shift = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+%28-pi%2F2%29+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+%28-pi%2F2%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians  (= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-90%5Eo ALIGN=MIDDLE  ALT=\"-90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > )  (the shift is to the right)\r<BR>\n" );
document.write( "\n" );
document.write( "—<BR>\n" );
document.write( "Update:  After seeing Edwin's answer, I must admit that I missed absolute value of A as amplitude, so it is |A| = amplitude.   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );