Question 858549
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(x)\ +\ \sin(x)\ -\ 1\ =\ 0]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2u^2\ +\ u\ -\ 1\ =\ 0]


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2u\ -\ 1)(u\ +\ 1)\ =\ 0]


Then *[tex \Large \sin(x ) \ =\ \frac{1}{2}] or *[tex \Large \sin(x)\ =\ -1]


Find your values on the unit circle.  There are two solutions for *[tex \Large \sin(x ) \ =\ \frac{1}{2}] and one solution for *[tex \Large \sin(x)\ =\ -1] in the desired interval.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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