Question

I = cos(wt)+sqrt(3)sin(wt)

I need to find the max and min points. I know that the answers are I max = 2 and I min = -2 , but I do not know how to show the work.

Answer 1

You can use a trigonometric identity, where\[{a}\sin(x)+{b}\cos(x)={r}\sin(x+\alpha)\]where \[r=\sqrt{a^2+b^2}\]and\[\tan{\alpha}=\frac{b}{a}\]
In your case, you would identify \[a=\sqrt{3}\]and\[b=1\]so that \[r=2\]and \[\tan{\alpha}=\frac{1}{\sqrt{3}} \rightarrow \alpha=30^o\]so that\[\cos(\omega{t})+\sqrt{3}\sin(\omega{t})=2\sin(\omega{t}+30^o)\]Now all you have to do is apply what you know of trigonometric functions and amplitude. The sine of *anything* oscillates between +1 and -1, so if sine is multiplied by 2, the maximum and minimum values of 2*sine will be +2 and -2 respectively.