document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141704>Question 1141704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write a cosine function with amplitude 3 and period pi/2 which has been shifted up 1 unit.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762301 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=762301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "With no horizontal shift, a general cosine function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a%2Acos%28bx%29%2Bd ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%2Acos%28bx%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where a is the amplitude, b determines the period, and d is the vertical shift.<br><BR>\n" );
document.write( "In this problem the amplitude is 3 and the vertical shift is +1, so the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3%2Acos%28bx%29%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29+=+3%2Acos%28bx%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the value of the parameter b, note that the basic cosine function has a period of 2pi while the given function has a period of pi/2.  That means the function completes 4 cycles from 0 to 2pi; that means b is 4.<br><BR>\n" );
document.write( "(Algebraically, b is equal to 2pi divided by the period; in this example, (2pi)/(pi/2) = 4.)<br><BR>\n" );
document.write( "So<br><BR>\n" );
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