# math/calculus

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?

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1. 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

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2. 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?

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3. 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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