document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182153>Question 1182153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the graph below, determine a sine function and cosine function that can be used to represent the graph. Show all your work. \r<BR>\n" );
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document.write( "https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812151 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=812151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) Sine function<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;\" ><br><BR>\n" );
document.write( "d is the midline.  From the graph, d=3<br><BR>\n" );
document.write( "a is the amplitude -- positive difference between the midline and the maximum or minimum.  From the graph, a=3<br><BR>\n" );
document.write( "b determines the period; the period is 360/b.  On the graph, one period, as measured between consecutive maxima, is 60 degrees.  360/b=60, so b=6.<br><BR>\n" );
document.write( "c is the phase shift.  For a sine graph, at 0 the function is at the midline and increasing.  The graph shows this occurring at x=30 degrees, so the phase shift c is 30.<br><BR>\n" );
document.write( "We have a=3; b=6; c=30; d=3.  The function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sin%286%28x-30%29%29%2B3 ALIGN=MIDDLE  ALT=\"3sin%286%28x-30%29%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph (with the angle in radians)....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-pi%2F6%2Cpi%2C-2%2C8%2C3sin%286%28x-pi%2F6%29%29%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-pi%2F6%2Cpi%2C-2%2C8%2C3sin%286%28x-pi%2F6%29%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Cosine function<br><BR>\n" );
document.write( "<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( "Compared to the sine function, for the cosine function parameters a (amplitude), b (period), and d (midline) will be the same as for the sine function; the only parameter that is different is c (phase shift).<br><BR>\n" );
document.write( "For a cosine function, at 0 the function is at a maximum.  The graph shows the first maximum for a positive angle occurring at 45 degrees.  So for the cosine function the phase shift c is 45 degrees.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3cos%286%28x-45%29%29%2B3 ALIGN=MIDDLE  ALT=\"3cos%286%28x-45%29%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph (with the angle in radians)....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-pi%2F6%2Cpi%2C-2%2C8%2C3cos%286%28x-pi%2F4%29%29%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-pi%2F6%2Cpi%2C-2%2C8%2C3cos%286%28x-pi%2F4%29%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graphs of these sine and cosine functions are identical, and they are the same as the given graph.<br><BR>\n" );
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