document.write( "Question 1176031: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 96 degrees occurs at 4 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 7 AM. \n" ); document.write( "

Algebra.Com's Answer #801930 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "Outside temperature over a day can be modeled as a sinusoidal function.
\n" ); document.write( "Suppose you know the high temperature of 96 degrees occurs at 4 PM and
\n" ); document.write( "the average temperature for the day is 85 degrees.
\n" ); document.write( "Find the temperature, to the nearest degree, at 7 AM.
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document.write( "Our 24-hour cycle of the daily temperature change starts at 4 pm, when the temperature is maximal.\r\n" );
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document.write( "So, our sinusoidal function is, actually, the cosine function, if to start counting time from 4 pm = 16:00, or\r\n" );
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document.write( "    T(t) =  + \r\n" );
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document.write( "where \"t\" is the local astronomic time in the 24-hours \"military\" time scale in your watch.\r\n" );
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document.write( "At 7 am next day, we have   of the full cycle elapsed.\r\n" );
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document.write( "It corresponds to    on the unit circle, and   = - .\r\n" );
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document.write( "So, the temperature at 7 am  next day will be  \r\n" );
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document.write( "     =  = 85° - 0.707*11° = 77.2°.\r\n" );
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document.write( "ANSWER.  We can expect  77.2°, or 77° rounded at 7 am next day.\r\n" );
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