document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168728>Question 1168728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for each of the following functions find the amplitude the period and describe the horizontal and vertical shifts from relevant parent y =a sin(bx) or y = a cos(bx) note you do not need to draw the graph here <BR>\n" );
document.write( "1a) f(x) = -4cos[5(x+pi)] -2<BR>\n" );
document.write( "b f(x) = sin(x-pi/3)/2<BR>\n" );
document.write( "c f(x) = -sin(3x + pi/2) +1  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793369 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Fit each one into the standard form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asin%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"a%2Asin%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Acos%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"a%2Acos%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In that form...<br><BR>\n" );
document.write( "|a| is the amplitude (that is, the amplitude is always considered positive)<BR>\n" );
document.write( "b gives the period; the period is (2pi)/b<BR>\n" );
document.write( "c is the horizontal shift<BR>\n" );
document.write( "d is the vertical shift<br><BR>\n" );
document.write( "The only work you sometimes need to do is to get the \"x\" without a coefficient.  For example, if the definition includes \"sin(3x-pi)\", you need to change it to \"sin(3(x-pi/3))\".<br><BR>\n" );
document.write( "Also note that the inner parentheses must be in the form (x-c); if the given function shows (x+2), it has to be seen as (x-(-2)), making the horizontal shift -2.<br><BR>\n" );
document.write( "I'll do one similar example; you can do the ones you show in your post.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2cos%283x%2Bpi%29-3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2cos%283x%2Bpi%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rewrite it in standard form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2cos%283%28x-%28-pi%2F3%29%29%29-3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2cos%283%28x-%28-pi%2F3%29%29%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amplitude is |a| = |-2| = 2<BR>\n" );
document.write( "The period is (2pi)/b = (2pi)/3<BR>\n" );
document.write( "The horizontal shift is -pi/3<BR>\n" );
document.write( "The vertical shift is -3<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );