Question

An electric current, i, in amps, is given by i=cos(wt)+sqrt(6)sin(wt) where w≠0 is a constant. what are the maximum and minimum values of i?

Answer 1

First we should discuss some mathematical applications
If any equation y = asinФ + bcosФ are given
Then, y = $\bold{\sqrt{a^2+b^2}sin(x+tan^{-1}\frac{b}{a})}$
∴ range of y ∈ $[-\sqrt{a^2+b^2},\sqrt{a^2+b^2}]$
e.g., maximum value of y = $\sqrt{a^2+b^2}$
and minimum value of y = $-\sqrt{a^2+b^2}$

now use above application to solve this problem ,
Given I = cosωt + √6sinωt
∴ I = $\bold{\sqrt{1^2+\sqrt{6}^2}sin(\omega t + tan^{-1}\frac{1}{\sqrt{6}})}}$
Hence, maximum value of I = √7
Minimum value of I = -√7