document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188590>Question 1188590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question. \r<BR>\n" );
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document.write( "A curve has the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=acosbx%2Bc ALIGN=MIDDLE  ALT=\"y=acosbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,  with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E0 ALIGN=MIDDLE  ALT=\"a%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >   . Given that the range of the curve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%3E=y%3E=2 ALIGN=MIDDLE  ALT=\"-4%3E=y%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that the period of the curve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >, evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > .  Hence sketch the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C=360 ALIGN=MIDDLE  ALT=\"0%3C=x%3C=360\"   DISABLED_style= \"max-width:90%; height:auto;\" >  . \r<BR>\n" );
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document.write( "P.S. for before the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is a degrees sign it's just that I couldn't put it inside.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819717 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=819717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic form of the graph of the cosine function 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( "the frequency is equal to 360 divided by the period.\r<BR>\n" );
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document.write( "if the period is 180, then the frequency is 360 / 180 = 2.\r<BR>\n" );
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document.write( "the equation becomes y = a * (2 * (x - c)) + d.\r<BR>\n" );
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document.write( "i think you mean -4 <= y <= 2.\r<BR>\n" );
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document.write( "the graph of y usually has the negative value of y below the positive value of y.<BR>\n" );
document.write( "i haven't seen it the other way around.\r<BR>\n" );
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document.write( "since the range of y is from -4 to 2, then the total distance from the bottom of the cosine function to the top of the cosine function is 6.<BR>\n" );
document.write( "the center line of the cosine function therefore has to be in the middle, i.e. 3 from the top and 3 from the bottom.<BR>\n" );
document.write( "that  puts the center line of the horizontal line equal to -1.<BR>\n" );
document.write( "that makes d equal to 1.\r<BR>\n" );
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document.write( "the formula becomes y = a * (2 * (x - c)) - 1\r<BR>\n" );
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document.write( "it also makes the amplitude 6/3 = 3 because the amplitube is the distance from the horizontal center line of the graph.\r<BR>\n" );
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document.write( "the formula becomes y = 3 * (2 * (x - c)) - 1.\r<BR>\n" );
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document.write( "here does not appearw to be a horizontal shift, therefore c = 0 and is not shown.\r<BR>\n" );
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document.write( "the formula becomes y = 3 * (2 * x) + 1.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/120801.jpg\" >\r<BR>\n" );
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document.write( "most of the reference use radians rather than degrees.\r<BR>\n" );
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document.write( "here's what the graph looks like in radians.\r<BR>\n" );
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document.write( "the formula to convert from radians to degrees is degrees = radians * 180 / pi.\r<BR>\n" );
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document.write( "the formula to convert from degrees to radians is radians = degrees * pi / 180.\r<BR>\n" );
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document.write( "here's a reference on graph of the sine and cosine functions.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html\" target = \"_blank\">https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html</a>\r<BR>\n" );
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document.write( "here's another one.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/grphtrig.htm\" target = \"_blank\">https://www.purplemath.com/modules/grphtrig.htm</a>\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "looking at what you had versus what i have, your c looks to be my d.<BR>\n" );
document.write( "i could be wrong, but i didn't see any d in your version.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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