document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140741>Question 1140741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sinusoidal Functions<BR>\n" );
document.write( "Without graphing, determine the amplitude, period, equation of the axis, phase shift, domain, and range of the function y=20 cos(9x-81°)-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761250 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=761250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Acos%28b%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"y+=+a%2Acos%28b%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a is the amplitude<BR>\n" );
document.write( "360/b degrees is the period<BR>\n" );
document.write( "c is the positive phase shift  (that is, x-45 means shift 45 degrees to the right; x+60 (= x-(-60)) means shift 60 degrees to the left)<BR>\n" );
document.write( "d is the vertical shift<br><BR>\n" );
document.write( "Put your function in that form by factoring out the coefficient of x:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20%2Acos%289%28x-9%29%29-2 ALIGN=MIDDLE  ALT=\"y+=+20%2Acos%289%28x-9%29%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "amplitude: a = 20<BR>\n" );
document.write( "period: 360/b = 360/9 = 40 degrees<BR>\n" );
document.write( "phase shift: c = 9 degrees to the right<BR>\n" );
document.write( "vertical shift: d = -2, which means the axis (center line) is y=-2<BR>\n" );
document.write( "domain: all reals<BR>\n" );
document.write( "range: plus or minus 20 from the center line of -2, so -22 to +18 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );