document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203464>Question 1203464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the amplitude, midline, period, domain and range of each sinusoidal function<BR>\n" );
document.write( "then sketch a graph.<BR>\n" );
document.write( "y=3sin(x)+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839047 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general form of the sinusoidal equation is y = a * (b * (x - c)) + d<BR>\n" );
document.write( "a is the amplitude.<BR>\n" );
document.write( "b is the frequency.<BR>\n" );
document.write( "c is the horizontal shift.<BR>\n" );
document.write( "d is the vertical shift.\r<BR>\n" );
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document.write( "your equation is y = 3 * sin(x) + 4\r<BR>\n" );
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document.write( "the amplitude is 3.<BR>\n" );
document.write( "the frequency is 1.<BR>\n" );
document.write( "the horizontal shift is 0.<BR>\n" );
document.write( "the vertical shift is 4.\r<BR>\n" );
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document.write( "here is what the graph of the sine wave looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/090301.jpg\">\r<BR>\n" );
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document.write( "the horizontal center line of the graph is at y = 0 plus the vertical shift.<BR>\n" );
document.write( "tht makes y = 4 the center line of this graph.\r<BR>\n" );
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document.write( "the amplitude is the distance between the peak of the graph and the horizontal center line of the graph.<BR>\n" );
document.write( "the default amplitude is 1.<BR>\n" );
document.write( "when it is 3, the graph goes between y = 4 + 3 and y = 4 - 3 on this graph.<BR>\n" );
document.write( "that's y = 7 on the high peak and y = 1 on the low peak.\r<BR>\n" );
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document.write( "the frequency of  the graph is 1 unless otherwise specified.<BR>\n" );
document.write( "the normal period for a sine wave is 360 degrees.<BR>\n" );
document.write( "the frequency is 360 divided by the frequency.<BR>\n" );
document.write( "here it is 360 / 1 = 360 degrees.\r<BR>\n" );
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document.write( "the period of the sine wave is 360 divided by the freuency.<BR>\n" );
document.write( "since the frequency is 1, the period is 360 / 1 = 360 degrees.\r<BR>\n" );
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document.write( "the default values of y = a * sin(x - c)) + d are:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = 0<BR>\n" );
document.write( "d = 0<BR>\n" );
document.write( "they are implied, if not shown.<BR>\n" );
document.write( "for example;<BR>\n" );
document.write( "y = sin(x) has a = 1, b = 1, c = 0, and d = 0 implied.<BR>\n" );
document.write( "explicitly shown, it would be y = 1 * sin(1 * (x - 0)) + 0.\r<BR>\n" );
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document.write( "the domain of the graph is x = - infinity to x = + infinity.\r<BR>\n" );
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document.write( "here's a reference from the web.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html#:~:text=A%20sine%20wave%2C%20or%20sinusoid,the%20sine%20function%20in%20trigonometry.&text=(A%20and%20B%20are%20positive,such%20as%20science%20and%20engineering.\" target = \"_blank\">https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html#:~:text=A%20sine%20wave%2C%20or%20sinusoid,the%20sine%20function%20in%20trigonometry.&text=(A%20and%20B%20are%20positive,such%20as%20science%20and%20engineering.</a>\r<BR>\n" );
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document.write( "here is what several cycles of your sine wave look like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/090302.jpg\">\r<BR>\n" );
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