Question

please help: an AC-DC coupled circuit produces a current described by the function I(t) = 60cost+25. where t is time, in seconds, and I is the current, in amperes, at time t.
Find the max and min currents and the times at which they occur

Answer 1

calc and then set dI/dt to 0 and see where you get to.

Answer 2

d/dt(cos{t}) = ???

Answer 3

it equals to -60sint

Answer 4

Intuitively, each time \(\cos t=1\) we've reached a maximum, and each time \(\cos t=-1\) we've reached a minimum.

Answer 5

$$l(t) = 60\cos t+25\\-60+25\le l(t)\le 60+25\\-35\le l(t)\le85$$...so we've found our extrema values. To find out where they happen, ask yourself: when will \(\cos t=1\)? what about \(\cos t=-1\)?

Answer 6

@0202

so -60sint(t) = 0 implies that sin(t) = 0 is where the peaks and troughs occur.
now, sin(t) = 0 when t = 0, t = 180deg, t= 360deg;
or, better, in radians, when t = 0, t = π, t = 2π, and so on

so, plug these numbers into the original equation:
I(t) = 60cos(0) + 25 = 85
I(t) = 60cos(π) + 25 = -35
I(t) = 60cos(2π) + 25 = 85
I(t) = 60cos(3π) + 25 = -35

Answer 7

@IrishBoy123 why complicate with calculus when it's intuitive?

Answer 8

i think calculus is intuitive.