Question 1118055
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(x)\ +\ 7\cos(x)\ =\ 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\(1\ -\ \cos^2(x)\)\ +\ 7\cos(x)\ -\ 5\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2(x)\ -\ 7\cos(x)\ +\ 3\ =\ 0]


Let *[tex \Large u\ =\ \cos(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2u^2\ -\ 7u\ +\ 3\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2u\ -\ 1)(u\ -\ 3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u\ =\ \frac{1}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u\ =\ 3]


Substitute back


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ \frac{1}{2}]


But *[tex \LARGE -1\ \leq\ \cos(x)\ \leq\ 1], so discard *[tex \LARGE \cos(x)\ =\ 3]


*[illustration unit_circle11_43203_lg.jpg]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^{-1}\(\frac{1}{2}\)\ =\ \frac{\pi}{3}]


Or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^{-1}\(\frac{1}{2}\)\ =\ \frac{5\pi}{3}] 


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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