document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079785>Question 1079785</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Use a reference rectangle and the rule of fourths to draw an accurate sketch of the following function through at least one full cycle.\r<BR>\n" );
document.write( "\n" );
document.write( "y = 5 sin t<BR>\n" );
document.write( "i have here the choices to choose from but I can't attach a picture here :-( Please help me to draw a sketch </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #694036 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=694036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
document.write( "\n" );
document.write( "note: general formulas\r<BR>\n" );
document.write( "\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Asin%28b%2Ax%29 ALIGN=MIDDLE  ALT=\"y+=+a%2Asin%28b%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2A+cos%28b%2Ax%29 ALIGN=MIDDLE  ALT=\"y+=+a%2A+cos%28b%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > in both of the following graph types affects the period (or wavelength) of the graph.\r<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=period ALIGN=MIDDLE  ALT=\"period\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance (or time) that it takes for the sine or cosine curve to begin repeating again. \r<BR>\n" );
document.write( "\n" );
document.write( "Frequency is defined as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=frequency=1%2Fperiod ALIGN=MIDDLE  ALT=\"frequency=1%2Fperiod\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The relationship between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the period is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=period+=2pi%2Fb ALIGN=MIDDLE  ALT=\"period+=2pi%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: As <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets larger, the period <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=decreases ALIGN=MIDDLE  ALT=\"decreases\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives the number of cycles between  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > . Higher  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives higher frequency (and lower period).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Tip 1: The number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells us the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number ALIGN=MIDDLE  ALT=\"number\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cycles ALIGN=MIDDLE  ALT=\"cycles\"   DISABLED_style= \"max-width:90%; height:auto;\" > in each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "example:<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+10cos%28t%29%2C+there+is+%7B%7B%7Bone ALIGN=MIDDLE  ALT=\"y+=+10cos%28t%29%2C+there+is+%7B%7B%7Bone\"   DISABLED_style= \"max-width:90%; height:auto;\" > cycle between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >(because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+1 ALIGN=MIDDLE  ALT=\"b+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
document.write( "\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+10cos%283x%29 ALIGN=MIDDLE  ALT=\"y+=+10cos%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > cycles between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+3 ALIGN=MIDDLE  ALT=\"b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
document.write( "\n" );
document.write( "Tip 2: <BR>\n" );
document.write( "Remember, we are now operating using RADIANS. <BR>\n" );
document.write( "Recall that:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi=+6.283185 ALIGN=MIDDLE  ALT=\"2pi=+6.283185\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi=+360 ALIGN=MIDDLE  ALT=\"2pi=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's look at the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5sin%28+t%29 ALIGN=MIDDLE  ALT=\"y+=+5sin%28+t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "This time we have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=+5 ALIGN=MIDDLE  ALT=\"a=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=+5 ALIGN=MIDDLE  ALT=\"a=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is amplitude, so the curve goes up to 5 units and down to -5 units on the y-axis<BR>\n" );
document.write( " <BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F1=2pi ALIGN=MIDDLE  ALT=\"2pi%2F1=2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > (periodic in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > with period <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here is your sketch:\r<BR>\n" );
document.write( "\n" );
document.write( "http://www.intmath.com/trigonometric-graphs/svg/svgphp-graphs-sine-cosine-amplitude-1-s1.svg\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );