document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607375>Question 607375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The depth of the water at the end of a boat dock is given by:\r<BR>\n" );
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document.write( "y=3sin[2pi/12 (x+3)] +9, where x is the number of hours after midnight.\r<BR>\n" );
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document.write( "a. What is the amplitude?<BR>\n" );
document.write( "b. What is the period?<BR>\n" );
document.write( "c. What is the phase shift?<BR>\n" );
document.write( "d. Sketch the graph of function for one full period starting with midnight. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382722 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=382722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The depth of the water at the end of a boat dock is given by: <BR>\n" );
document.write( "y=3sin[2pi/12 (x+3)] +9, where x is the number of hours after midnight. <BR>\n" );
document.write( "a. What is the amplitude?<BR>\n" );
document.write( "b. What is the period?<BR>\n" );
document.write( "c. What is the phase shift?<BR>\n" );
document.write( "d. Sketch the graph of function for one full period starting with midnight<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Equation of sin function: Asin(Bx-C), A=amplitude, Period=2&#960;/B, Phase shift=C/B<BR>\n" );
document.write( "Rewrite given equation:<BR>\n" );
document.write( "y=3sin[2pi/12 (x+3)] +9<BR>\n" );
document.write( "=3sin[&#960;/6 (x+3)] +9<BR>\n" );
document.write( "=3sin[&#960;x/6+&#960;/2] +9<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Amplitude=3<BR>\n" );
document.write( "B=&#960;/6<BR>\n" );
document.write( "Period=2&#960;/B=2&#960;/(&#960;/6)=12 hrs<BR>\n" );
document.write( "1/4 period=3<BR>\n" );
document.write( "C=&#960;/2<BR>\n" );
document.write( "Phase shift=C/B=(&#960;/2)/(&#960;/6)=3 hrs (shift left)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Graph function for one period:<BR>\n" );
document.write( "I don't have the means to draw a graph but I will develop the (x,y) coordinates with which you can use  to draw a graph for one period. <BR>\n" );
document.write( "..<BR>\n" );
document.write( "Start with coordinates of basic sin function: sin(&#960;x/6) (x-axis scaled in hours)<BR>\n" );
document.write( "(0,0), (3,1), (6,0), (9,-1), (12,0)<BR>\n" );
document.write( "Include amplitude: 3sin(&#960;x/6)<BR>\n" );
document.write( "(0,0), (3,3), (6,0), (9,-3), (12,0)<BR>\n" );
document.write( "Shift 3 hrs left: 3sin(&#960;x/6+&#960;/2)<BR>\n" );
document.write( "(-3,0), (0,3), (3,0), (6,-3), (9,0),(12,3)<BR>\n" );
document.write( "Bump curve up 9 units:3sin(&#960;x/6+&#960;/2)+9 (final configuration)<BR>\n" );
document.write( "(-3,9), (0,12), (3,9), (6,6), (9,9), (12,12)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y-intercept<BR>\n" );
document.write( "set x=0<BR>\n" );
document.write( "y=3sin(&#960;x/6+&#960;/2)+9<BR>\n" );
document.write( "y=3(sin&#960;/2)+9<BR>\n" );
document.write( "y=3*1+9=12<BR>\n" );
document.write( "You now have the y-intercept and the (x,y) coordinates with which you can draw graph of given sin function. One full period starts at (0,12) and ends at (12,12)<BR>\n" );
document.write( " </SPAN>\n" );
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