document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=689126>Question 689126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when compared to y=sin(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425867 by </B><A HREF=/tutors/aboutme.mpl?userid=exodus><B>exodus(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=exodus><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=425867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general equation that should be formed is as follows:\r<BR>\n" );
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document.write( "y - A = Bsin(x - C)\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "A stands for a vertical shift (if A is positive, move is upward; if A is negative, move is downward)\r<BR>\n" );
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document.write( "B stands for vertical stretch factor \r<BR>\n" );
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document.write( "C stands for a horizontal shift (if C is positive, move is to the right; if C is negative, move is to the left).\r<BR>\n" );
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document.write( "We start with the sine wave in 'home' position, having equation y = sin(x) which is really as follows:\r<BR>\n" );
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document.write( "y - 0 = 1sin(x - 0)\r<BR>\n" );
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document.write( "with \r<BR>\n" );
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document.write( "A = 0, (no vertical shift or change)\r<BR>\n" );
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document.write( "B = 1, (normal stretch factor or 'amplitude')\r<BR>\n" );
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document.write( "C = 0, (no horizontal shift or change)\r<BR>\n" );
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document.write( "so, the equation required is as follows:\r<BR>\n" );
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document.write( "y - (-8) = 4sin(x - 9) \r<BR>\n" );
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document.write( "which can simplify to\r<BR>\n" );
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document.write( "y + 8 = 4sin(x - 9)\r<BR>\n" );
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document.write( "or, if final equation is given in the form \"y in terms of x\" (also called 'making y the subject'), then:\r<BR>\n" );
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document.write( "y = 4sin(x - 9) - 8\r<BR>\n" );
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document.write( " </SPAN>\n" );
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