document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091306>Question 1091306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the curve y=sin(1/2thetha-90 degrees)-4   state the following information. 				\r<BR>\n" );
document.write( "\n" );
document.write( "	phase shift   ________       amplitude  ________ 	vertical displacement  ______\r<BR>\n" );
document.write( "\n" );
document.write( "	max y–value  ________      min y–value   ____________    period  _________<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705736 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sin%281%2F2%28theta%29-90+%29-4+ ALIGN=MIDDLE  ALT=\"y=sin%281%2F2%28theta%29-90+%29-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Use the form<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2Asin%28bx-c%29%2Bd ALIGN=MIDDLE  ALT=\"+a%2Asin%28bx-c%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the variables used to find the amplitude, period, phase shift, and vertical shift.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F2 ALIGN=MIDDLE  ALT=\"b=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=90+ ALIGN=MIDDLE  ALT=\"c=90+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+ ALIGN=MIDDLE  ALT=\"pi%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >radians<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-4 ALIGN=MIDDLE  ALT=\"d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the amplitude is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=1 ALIGN=MIDDLE  ALT=\"a+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, amplitude is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Find the period using the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Fb ALIGN=MIDDLE  ALT=\"2pi%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F%281%2F2%29=4pi ALIGN=MIDDLE  ALT=\"2pi%2F%281%2F2%29=4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "period :<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+pi ALIGN=MIDDLE  ALT=\"4+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Find the phase shift using the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fb ALIGN=MIDDLE  ALT=\"c%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2F2%29%2F%281%2F2%29=2pi%2F2=pi ALIGN=MIDDLE  ALT=\"%28pi%2F2%29%2F%281%2F2%29=2pi%2F2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >->\r<BR>\n" );
document.write( "\n" );
document.write( " the phase shift : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " the vertical shift is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-4 ALIGN=MIDDLE  ALT=\"d=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Vertical Shift:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units down\r<BR>\n" );
document.write( "\n" );
document.write( "max<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%28theta%2F2+-+90%29+-+4+=+-3+ ALIGN=MIDDLE  ALT=\"y+=+sin%28theta%2F2+-+90%29+-+4+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+180+%2B+pi+-+4+n+%2Api+ ALIGN=MIDDLE  ALT=\"theta+=+180+%2B+pi+-+4+n+%2Api+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "min<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%28theta%2F2+-+90%29+-+4+=+-5 ALIGN=MIDDLE  ALT=\"y+=+sin%28theta%2F2+-+90%29+-+4+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+180+-+pi+-+4+n+%2Api ALIGN=MIDDLE  ALT=\"theta+=+180+-+pi+-+4+n+%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "answer:\r<BR>\n" );
document.write( "\n" );
document.write( "phase shift ____<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >____ amplitude ___<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >_____ vertical displacement ___<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units down___<BR>\n" );
document.write( "max y–value ___<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+ ALIGN=MIDDLE  ALT=\"-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >_____ min y–value ____<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >________ period ___<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+pi ALIGN=MIDDLE  ALT=\"4+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >______\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );