document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205033>Question 1205033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph represents a sine function in the form<BR>\n" );
document.write( "y = A sin B(t + C) + D or a cosine function in the form y = A cos B(t + C) + D. Write both equations for each.\r<BR>\n" );
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document.write( "Answer key: y = 4 sin πt, y = 4 cos π(t  -  1/2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.ibb.co/Tgw12T5/x.png\">\r<BR>\n" );
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document.write( "By the way, is there an edit button or similar function to make changes to a post after I've already posted it in case I discover later on I've made a typo? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841632 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=841632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The graph represents a sine function in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A+sin+B%28t+%2B+C%29+%2B+D ALIGN=MIDDLE  ALT=\"y+=+A+sin+B%28t+%2B+C%29+%2B+D\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "or a cosine function in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A+cos+B%28t+%2B+C%29+%2B+D ALIGN=MIDDLE  ALT=\"y+=+A+cos+B%28t+%2B+C%29+%2B+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Write both equations for each.\r<BR>\n" );
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document.write( "from the graph we see that amplitude is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we also see that the mid line  is x-axis, so the graph is not shifted vertically and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "there is also no horizontal shift, so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C=0 ALIGN=MIDDLE  ALT=\"+C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the graph passes through the origin, the graph of a sine function always intersect the mid line (which is x-axis in your case) at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have sine function\r<BR>\n" );
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document.write( "so, we will use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+A+sin+B%28t+%2B+C%29+%2B+D ALIGN=MIDDLE  ALT=\"y+=+A+sin+B%28t+%2B+C%29+%2B+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=0 ALIGN=MIDDLE  ALT=\"C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4sin%28+B%28t+%29%29 ALIGN=MIDDLE  ALT=\"y+=+4sin%28+B%28t+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "one full cycle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units, so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B=2 ALIGN=MIDDLE  ALT=\"+B=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2FB=2pi%2F2=pi ALIGN=MIDDLE  ALT=\"2pi%2FB=2pi%2F2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4sin%28+pi%2At%29 ALIGN=MIDDLE  ALT=\"y+=+4sin%28+pi%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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