An electric current, i, in amps, is given by i=cos(wt)+√8sin(wt), where w≠0 is a constant. what are the maximum and minimum values of i

Take the derivative with respect to t

the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero

divide by w

we add sin(wt) to both sides


divide both sides by cos(wt)
OR
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be


since 2npi is just the period of cos

substituting our second soultion we get

since 2npi is the period

so the maximum value =
minimum value =