document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040749>Question 1040749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello amazing tutors, can you help me solve this pleasee, thank youuu\r<BR>\n" );
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document.write( "(i)Sketch the graph of the curve y = 3 sin x, for &#8722;&#960; &#8804; x &#8804; &#960;\r<BR>\n" );
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document.write( "The straight line y = kx, where k is a constant, passes through the maximum point of this curve for &#8722;&#960; &#8804; x &#8804; &#960; .<BR>\n" );
document.write( "(ii) Find the value of k in terms of &#960;<BR>\n" );
document.write( "(iii) State the coordinates of the other point, apart from the origin, where the line and the curve<BR>\n" );
document.write( "intersect </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655652 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The basic facts you need to know about<BR>\n" );
document.write( "the sine curve is:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28x%29+ ALIGN=MIDDLE  ALT=\"+sin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > repeats itself every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2pi+ ALIGN=MIDDLE  ALT=\"+2pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "radians<BR>\n" );
document.write( "(2) the maximum value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28x%29+ ALIGN=MIDDLE  ALT=\"+sin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and this maximum occurs every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2F2+%2B-+2pi+ ALIGN=MIDDLE  ALT=\"+pi%2F2+%2B-+2pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "radians<BR>\n" );
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document.write( "(i), (ii), and (iii)<BR>\n" );
document.write( "You are given the interval &#8722;&#960; &#8804; x &#8804; &#960<BR>\n" );
document.write( "so, the only place where there is a maximum in this<BR>\n" );
document.write( "interval is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+pi%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+pi%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Your sine function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2Asin%28+x+%29+ ALIGN=MIDDLE  ALT=\"+3%2Asin%28+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the the maximum is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2A1+=+3+ ALIGN=MIDDLE  ALT=\"+3%2A1+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now you know the maximum point is at <BR>\n" );
document.write( "( pi/2, 3 )<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The straight line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+k%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+k%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" > must also pass through that<BR>\n" );
document.write( "point and also (0,0) since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+k%2A0+ ALIGN=MIDDLE  ALT=\"+y+=+k%2A0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you (0,0)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The slope, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3+-+0+%29+%2F+%28+pi%2F2+-+0+%29+=+6%2Fpi+ ALIGN=MIDDLE  ALT=\"+%28+3+-+0+%29+%2F+%28+pi%2F2+-+0+%29+=+6%2Fpi+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+6%2Fpi%29%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+%28+6%2Fpi%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Here are plots of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3%2Asin%28x%29+ ALIGN=MIDDLE  ALT=\"+y+=+3%2Asin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+6%2Fpi+%29%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+%28+6%2Fpi+%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+800%2C+-pi%2C+pi%2C+-4%2C+4%2C+3%2Asin%28x%29+%2C+%286%2Fpi%29%2Ax+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+800%2C+-pi%2C+pi%2C+-4%2C+4%2C+3%2Asin%28x%29+%2C+%286%2Fpi%29%2Ax+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );