document.write( "Question 1183251: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 90 degrees and the low temperature of 80 degrees occurs at 6 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.\r
\n" ); document.write( "\n" ); document.write( "D(t)=\r
\n" ); document.write( "\n" ); document.write( "How do i go about this question \n" ); document.write( "

Algebra.Com's Answer #813475 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Outside temperature over a day can be modelled as a sinusoidal function.
\n" ); document.write( "Suppose you know the high temperature for the day is 90 degrees and the low temperature of 80 degrees occurs at 6 AM.
\n" ); document.write( "Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
\n" ); document.write( "D(t)=
\n" ); document.write( "How do i go about this question
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The difference between the highest and lowest temperature is 90 - 80 = 10 degrees;  \r\n" );
document.write( "\r\n" );
document.write( "hence, the midline is 85 degrees and the amplitude is   = 5 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, if x is the time starting from 6 am (x= 0 when the temperature is lowest), then OBVIOUSLY, the temperature as a function of x is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    D(x) =       (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(we use the sign  \" - \"  to reflect cosinusoid about the midline, and we use the ratio x/24 to model the period of 24 hours).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now, if t is the time after midnight, then x = t-6,  so the formula (1) takes the final form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    D(t) = .        ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Or, if you like to use degrees instead of radians, then the same formula takes an EQUIVALENT form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    D(t) = .          ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=============\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "How tutor @Theo solved the problem, is a formal presentation; but as far as I know, in reality, \r
\n" ); document.write( "\n" ); document.write( "nobody solves such problems in this way, and (in my opinion) it is not a good way to teach students.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I am 100% convinced that after such teaching, although formally it is right, the students' understanding will be ZERO.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "What I showed you in my post, is a way to solve such problems using common sense \r
\n" ); document.write( "\n" ); document.write( "(combined with the knowledge of elementary Trigonometry). I hope, it is much more educative.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );