document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203489>Question 1203489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the exact maximum and minimum y-values and their corresponding x-values for one period where <BR>\n" );
document.write( "x > 0.<BR>\n" );
document.write( " (For each answer, use the first occurrence for which <BR>\n" );
document.write( "x > 0.)<BR>\n" );
document.write( " f(x)=5sin(x-5pi/6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839098 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The min and max of y = sin(x) are y = -1 and y = 1 respectively.<BR>\n" );
document.write( "This would apply even if the input x is replaced with any expression such as x - 5pi/6\r<BR>\n" );
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document.write( "Sticking a 5 out front will vertically stretch the graph. <BR>\n" );
document.write( "This would mean the min and max of y = 5*sin(x-5pi/6) are y = -5 and y = 5 respectively. <BR>\n" );
document.write( "Use a graphing tool like a TI83, Desmos, or GeoGebra to confirm this claim. \r<BR>\n" );
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document.write( "Let's replace y with -5 and solve for x.<BR>\n" );
document.write( "y = 5*sin(x-5pi/6)<BR>\n" );
document.write( "-5 = 5*sin(x-5pi/6)<BR>\n" );
document.write( "-5/5 = sin(x-5pi/6)<BR>\n" );
document.write( "-1 = sin(x-5pi/6)<BR>\n" );
document.write( "x-5pi/6 = arcsin(-1) or x-5pi/6 = pi - arcsin(-1)<BR>\n" );
document.write( "x-5pi/6 = 3pi/2 or x-5pi/6 = pi - 3pi/2<BR>\n" );
document.write( "x-5pi/6 = 3pi/2 or x-5pi/6 = 2pi/2 - 3pi/2<BR>\n" );
document.write( "x-5pi/6 = 3pi/2 or x-5pi/6 = -pi/2<BR>\n" );
document.write( "x = 3pi/2+5pi/6 or x = -pi/2+5pi/6<BR>\n" );
document.write( "x = 9pi/6+5pi/6 or x = -3pi/6+5pi/6<BR>\n" );
document.write( "x = 14pi/6 or x = 2pi/6<BR>\n" );
document.write( "x = 7pi/3 or x = pi/3\r<BR>\n" );
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document.write( "Because 1 < 7, it leads to pi < 7pi and further pi/3 < 7pi/3<BR>\n" );
document.write( "pi/3 is the smaller of the two values.\r<BR>\n" );
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document.write( "This is the first occurrence when we reach the min y = -5 such that x > 0.\r<BR>\n" );
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document.write( "To find when the max y = 5 first occurs, plug in y = 5 and follow similar steps as shown above.<BR>\n" );
document.write( "After doing so, you should find that x = 4pi/3 is the first x value to reach the max y = 5 when x > 0.\r<BR>\n" );
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document.write( "The graphing tools I mentioned earlier can be used to confirm the answers. <BR>\n" );
document.write( "Various online calculators can be helpful as well. <BR>\n" );
document.write( "I recommend that you do the actual scratch work yourself and use the calculators to check your answers (or else you won't be ready for the exams later).\r<BR>\n" );
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document.write( "<font color=red size=4>Summary</font><BR>\n" );
document.write( "Min and max are y = -5 and y = 5<BR>\n" );
document.write( "First min occurs when x = pi/3<BR>\n" );
document.write( "First max occurs when x = 4pi/3<BR>\n" );
document.write( "In other words, the location of the first min is (pi/3, -5) when x > 0.<BR>\n" );
document.write( "The location of the first max is (4pi/3, 5) when x > 0.\r<BR>\n" );
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document.write( "Graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-7%2C7%2C-7%2C7%2C%0D%0Agraph%28400%2C400%2C-7%2C7%2C-7%2C7%2C-1000%2C5%2Asin%28x-5pi%2F6%29%29%2C%0D%0A%0D%0Acircle%281.04719755%2C-5%2C0.1%29%2Ccircle%281.04719755%2C-5%2C0.12%29%2Ccircle%281.04719755%2C-5%2C0.14%29%2Ccircle%281.04719755%2C-5%2C0.16%29%2Ccircle%284.18879020%2C5%2C0.1%29%2Ccircle%284.18879020%2C5%2C0.12%29%2Ccircle%284.18879020%2C5%2C0.14%29%2Ccircle%284.18879020%2C5%2C0.16%29%2C%0D%0A%0D%0Alocate%281.2472%2C-5.2%2C%22A%22%29%2Clocate%284.58879%2C5.4%2C%22B%22%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = first local min = (pi/3, -5) when focusing on the interval x > 0<BR>\n" );
document.write( "B = first local max = (4pi/3, 5) when focusing on the interval x > 0<BR>\n" );
document.write( "pi/3 = 1.04719755 approximately<BR>\n" );
document.write( "4pi/3 = 4.18879020 approximately\r<BR>\n" );
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