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## anonymous 5 years ago 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.

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1. anonymous

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.

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