document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534597>Question 534597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch on a graph 2 periods of y=150sin(4x-Pi)in radians </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351713 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=351713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sketch on a graph 2 periods of y=150sin(4x-&#960;)in radians<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Equation used to graph sin function: y=Asin(Bx-C), A=amplitude, Period =2&#960;/B, C/B=Phase shift<BR>\n" );
document.write( "For given sin function:<BR>\n" );
document.write( "A=150<BR>\n" );
document.write( "B=4<BR>\n" );
document.write( "Period: 2&#960;/B=2&#960;/4=&#960;/2<BR>\n" );
document.write( "1/4 period=&#960;/8<BR>\n" );
document.write( "Phase shift:C/B=&#960;/4 (shift to right)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Graphing: (For 2 periods)<BR>\n" );
document.write( "Let us first graph the basic sin function for 2 periods<BR>\n" );
document.write( "On the x-axis make tick marks at &#960;/8, &#960;/4, 3&#960;/8, &#960;/2, 5&#960;/8, 3&#960;/4, 7&#960;/8, &#960;, representing 2 periods.<BR>\n" );
document.write( "This will give you the following points:<BR>\n" );
document.write( "(0,0), (&#960;/8,1), (&#960;/4,0), (3&#960;/8-1), (&#960;/2,0), (5&#960;/8,1), (3&#960;/4,0), (7&#960;/8,-1), (&#960;,0)<BR>\n" );
document.write( "multiply the y-coordinates by 150<BR>\n" );
document.write( "(0,0), (&#960;/8,150), (&#960;/4,0), (3&#960;/8-150), (&#960;/2,0), (5&#960;/8,150), (3&#960;/4,0), (7&#960;/8,-150), (&#960;,0)<BR>\n" );
document.write( "add &#960;/4 to the x-coordinates (shifting the curve &#960;/4 to the right)<BR>\n" );
document.write( "(&#960;/4,0), (3&#960;/8,150), (&#960;/2,0), (5&#960;/8,-150), (3&#960;/4,0), (7&#960;/8,150), (&#960;,0), (9&#960;/8,-150), (5&#960;/4,0)<BR>\n" );
document.write( "y-intercept<BR>\n" );
document.write( "set x=0<BR>\n" );
document.write( "0=150(sin (-&#960;))=0<BR>\n" );
document.write( "y-intercept=0<BR>\n" );
document.write( "You now have all these points and the y-intercept with which you can graph the function. The graph should start from the origin. So the following is the final configuration:<BR>\n" );
document.write( "(0,0), (&#960;/8,-150), (&#960;/4,0), (3&#960;/8,150), (&#960;/2,0), (5&#960;/8,-150), (3&#960;/4,0),(7&#960;/8,150), (&#960;,0), (9&#960;/8,-150), (5&#960;/4,0)<BR>\n" );
document.write( "The x-coordinates are numbers(radians) with decimals; ie, &#960;/8&#8776;.3927, 3&#960;/8&#8776;1.1781, etc. Use &#960;=3.14<BR>\n" );
document.write( "Note that the period of given sin function=&#960;/2<BR>\n" );
document.write( "A phase shift of &#960;/4 shifts the curve half a period to the right </SPAN>\n" );
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