document.write( "Question 1189998: The current i (in amperes) at time t in a particular circuit is given by
\n" ); document.write( "i =12sin t + 5cost.
\n" ); document.write( "Find the maximum current and the first time that it occurs. \n" ); document.write( "

Algebra.Com's Answer #821532 by ikleyn(52817) $\"\"$ $\"About$

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\n" ); document.write( "The current i (in amperes) at time t in a particular circuit is given by
\n" ); document.write( "i =12sin t + 5cost.
\n" ); document.write( "Find the maximum current and the first time that it occurs.
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document.write( "Doing it in the Calculus frame, take the derivative  ;  equate it to zero and find the time\r\n" );
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document.write( "The derivative is   = 12cos(t) - 5sin(t).\r\n" );
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document.write( "The equation   = 0  is  12cos(t) - 5sin(t) = 0,  or  12cos(t) = 5sin(t),  which gives\r\n" );
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document.write( "     = ,  or  tan(t) = ,\r\n" );
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document.write( "Hence,  t = arctan(12/5) = 1.176 units of time.   It is the first occurrence time of the maximum.     ANSWER\r\n" );
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document.write( "           Since everything happens in the 1st quadrant, \r\n" );
document.write( "       where both sin(t) and cos(t) are positive, it is clear\r\n" );
document.write( "          that the found extremum is indeed the maximum\r\n" );
document.write( "       (not a minimum), and a special check is not needed.\r\n" );
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document.write( "Next, from tan(t) = ,  we have  sin(t) =  = ;\r\n" );
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document.write( "                                   cos(t) = .\r\n" );
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document.write( "Substituting these values for sin(t) and cos(t) into the formula for \"i\", we obtain the value of  \r\n" );
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document.write( "     =  +  =  =  = 13 amperes.    ANSWER.\r\n" );
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