(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a solutuion to a differential equation I've solved:

[tex] -cos(\sqrt(2)t) - 2sin(\sqrt(2)t) [/tex]

I've been asked to put it in the form:

[tex] Asin(wt + phi) [/tex]

2. Relevant equations

[tex] A= sqrt(-1^2 + -2^2) [/tex]

[tex] phi = sin^{-1}phi = \frac{c1}{A} [/tex]

[tex] phi = cos^{-1} phi = \frac{c2}{A} [/tex]

and

[tex] phi = tan^{-1} phi = \frac{c1}{c2} [/tex]

3. The attempt at a solution

A = 5

[tex] phi = sin^{-1}phi = \frac{-1}{\sqrt(5)} [/tex]

[tex] phi = -0.4636[/tex]

[tex] phi = cos^{-1} phi = \frac{-2}{\sqrt(5)} [/tex]

[tex] phi = 2.678[/tex]

and

[tex] phi = tan^{-1} phi = \frac{-1}{-2} [/tex]

[tex] phi = 0.4636[/tex]

Can you help with the phase angle? (3 different answers - none of which are correct)

The book has 3.6052 which I see is pi + 0.4636.

Thanks

-Sparky

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