document.write( "Question 1188816: Determine the smaller angle (Ac) formed by the hands of the clock at 3:30 PM. Give the angle coterminal with angle Ac such that Ac is greater than or equal to 360 degrees and smaller than 720 degrees. \n" ); document.write( "
Algebra.Com's Answer #819994 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "There are 60 minute graduations around the 360 degree clock face, so the minute\r\n" );
document.write( "graduations are 360/60 = 6 degrees apart.  Therefore the minute hand's angular\r\n" );
document.write( "speed is 6 degrees per minute.\r\n" );
document.write( "\r\n" );
document.write( "The minute hand rotates 12 times as fast as the hour hand, so the hour hand's\r\n" );
document.write( "angular speed is 1/12 as fast, or 6/12 = 1/2 = 0.5 degrees/minute. \r\n" );
document.write( "\r\n" );
document.write( "So the angle between the hands is increasing at 6.0-0.5 = 5.5 degrees per minute.  \r\n" );
document.write( "Every time the hands are exactly together they are 0 degrees or 360 degrees apart. \r\n" );
document.write( "\r\n" );
document.write( "Notice that we can always add (or subtract) 360 degrees to (or from) any angle\r\n" );
document.write( "between the hands or between the vertical and either hand without incurring any\r\n" );
document.write( "difficulty.\r\n" );
document.write( "\r\n" );
document.write( "We will also use the formulas: \r\n" );
document.write( "\r\n" );
document.write( "Degrees rotated = (degrees per minute)(number of minutes) \r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( "Number of minutes = (degrees rotated)/(degrees per minute)\r\n" );
document.write( "\r\n" );
document.write( "----------------------\r\n" );
document.write( "\r\n" );
document.write( "Determine the smaller angle (Ac) formed by [BETWEEN] the hands of the clock at\r\n" );
document.write( "3:30 PM. Give the angle coterminal with angle Ac such that Ac is greater than or\r\n" );
document.write( "equal to 360 degrees and smaller than 720 degrees.\r\n" );
document.write( "\r\n" );
document.write( "The last time before 3:30 PM that we were certain of the position of the hands\r\n" );
document.write( "(without doing any calculating) was at exactly 3:00 PM.  At that instant, the\r\n" );
document.write( "minute hand was pointing precisely straight up and the hour hand was pointing\r\n" );
document.write( "precisely to the right and the angle between them was precisely 90 degrees or\r\n" );
document.write( "360-90=270 degrees or 270+360=630 degrees\r\n" );
document.write( "\r\n" );
document.write( "In 30 minutes' time, the angle between the hands changed at the rate of 5.5\r\n" );
document.write( "degrees per minute by 5.5(30)=165 degrees. So the angle between the hands at\r\n" );
document.write( "that time was 270+165=435. [Essentially the hands were 435-360=75 degrees apart\r\n" );
document.write( "at 3:30.]\r\n" );
document.write( "\r\n" );
document.write( "So 435 degrees is the coterminal angle you were asked for.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );