Posted by miley on Tuesday, March 30, 2010 at 9:40pm.
an electric current I , in amps is given by:
I= cos(wt) + sqrt of 3 sin(wt)
where w is positive constant. what are the max and minimum values of I?
*please be specific
- math/calculus - Reiny, Tuesday, March 30, 2010 at 9:56pm
dI/dt = -wsin wt + w√3cos wt
= 0 for max min
wsin wt = w√3cos wt
sin wt/cos wt = w√3/w = √3
tan wt = pi/3 or 4pi/3
if wt = pi/3
I = cos pi/3 + √3sin pi/3 = .5 + 1.5 = 2
if wt = 4pi/3
I = cos 4pi/3 + √3sin 4pi/3 = -.5 -1.5 = -2
- math/calculus - miley, Tuesday, March 30, 2010 at 10:02pm
so it could be pi/3 or 4pi/3
which means both are correct?
should i put both answers or one answer on my final paper?
- math/calculus - Reiny, Tuesday, March 30, 2010 at 10:33pm
The pi/3 yields the maximum, notice I = +2
and the 4pi/3 yields the minimum
The actual question was, "what are the max and min values of I"
max of I is 2
min of I is -2
the pi/3 and 4pi/3 produce those max and mins, they themselves are not the max and mins.
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