document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208134>Question 1208134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q:1- What is the maximum and minimum value of Sin(x) + Cos(x)?<BR>\n" );
document.write( "Q;2- What is the maximum and minimum value of Sin(x) - Cos(x)?<BR>\n" );
document.write( "Q:3- What is the maximum and minimum value of Tan(x)/Sin(x) in [π/4 to π/3]?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846330 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=846330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll do question 1 to get you started.<BR>\n" );
document.write( "In the future please only post one question at a time.\r<BR>\n" );
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document.write( "If you are familiar with calculus, then,<BR>\n" );
document.write( "f(x) = sin(x) + cos(x)<BR>\n" );
document.write( "f ' (x) = cos(x) - sin(x) ..... apply derivative\r<BR>\n" );
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document.write( "The local max occurs when f ' (x) = 0.<BR>\n" );
document.write( "cos(x) - sin(x) = 0<BR>\n" );
document.write( "cos(x) = sin(x)<BR>\n" );
document.write( "Use the unit circle to determine that the sine and cosine values are equal when x = pi/4 when in quadrant I. \r<BR>\n" );
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document.write( "Use this x value to determine the max value of f(x).<BR>\n" );
document.write( "f(x) = sin(x) + cos(x)<BR>\n" );
document.write( "f(pi/4) = sin(pi/4) + cos(pi/4)<BR>\n" );
document.write( "f(pi/4) = sqrt(2)/2 + sqrt(2)/2<BR>\n" );
document.write( "f(pi/4) = sqrt(2)\r<BR>\n" );
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document.write( "sqrt(2) is the max value of sin(x)+cos(x).<BR>\n" );
document.write( "Through symmetry, the min value of that expression is -sqrt(2)\r<BR>\n" );
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document.write( "sqrt(2) = 1.41421 approximately\r<BR>\n" );
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document.write( "If you are not familiar with calculus, then you'll need to rely solely on a graphing calculator. <BR>\n" );
document.write( "The graphing calculator should have functions called \"minimum\" and \"maximum\". \r<BR>\n" );
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document.write( "Here is an article that talks about finding the local min and max on a TI84<BR>\n" );
document.write( "https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/04%3A_Introduction_to_the_TI-84/4.02%3A_Finding_zeros_maxima_and_minima\r<BR>\n" );
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document.write( "Another approach is shown here<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1046265.html<BR>\n" );
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