document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241983>Question 241983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem:<BR>\n" );
document.write( "Which of the following equations has amplitude=-2 period=pi/4,phase shift=-pi/2? <BR>\n" );
document.write( "THIS ARE THE POSSIBLE ANSWERS:<BR>\n" );
document.write( "a)y=-2cos8(x-pi/2)<BR>\n" );
document.write( "b)y=-2cos8(x+pi/2)<BR>\n" );
document.write( "c)y=-2cos4(x+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 #177192 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=177192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A general form for sin and cos functions is:<BR>\n" );
document.write( "y = C + A*sin(B(x - D))<BR>\n" );
document.write( "or<BR>\n" );
document.write( "y = C + A*cos(B(x - D))<BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29 ALIGN=MIDDLE  ALT=\"abs%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Amplitude. So A = 2 or -2.<BR>\n" );
document.write( "B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >/period<BR>\n" );
document.write( "C = Vertical shift<BR>\n" );
document.write( "D = Horizontal (or phase) shift<br><BR>\n" );
document.write( "You are given the amplitude so you know A. You are given the period so we can figure out B:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%282pi%29%2F%28pi%2F4%29 ALIGN=MIDDLE  ALT=\"B+=+%282pi%29%2F%28pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+8 ALIGN=MIDDLE  ALT=\"B+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are not given a vertical shift so we will use 0 for C. And you are give the phase shift so D = <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;\" >.<br><BR>\n" );
document.write( "So now we just find the equation that fits the A, B, C and D the we found above. It should be clear that equation (a) is correct.<br><BR>\n" );
document.write( "(BTW: The -2 for A means that the amplitude is 2 and, because of the minus, the graph is reflected about the x-axis.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );