Question 1064091
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Can't answer this the way you have the answer selections worded.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan^2(x)\ -\ \tan(x)\ =\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan^2(x)\ -\ \tan(x)\ -\ 2\ =\ 0]


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan(x)\ =\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan^{-1}(2)\ \approx\ 63.435^\circ\ \pm\ k180^\circ] where *[tex \LARGE k\ \in\ \mathbb{Z}]


So in the interval *[tex \LARGE 0^\circ\ \leq\ x\ <\ 360^\circ], *[tex \LARGE \tan^{-1}(2)\ \approx\ 63.435^\circ] or *[tex \LARGE \tan^{-1}(2)\ \approx\ 243.435^\circ]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan(x)\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan^{-1}(-1)\ =\ 135^\circ\ \pm\ k180^\circ] where *[tex \LARGE k\ \in\ \mathbb{Z}]


So in the interval *[tex \LARGE 0^\circ\ \leq\ x\ <\ 360^\circ], *[tex \LARGE \tan^{-1}(-1)\ =\ 135^\circ] or *[tex \LARGE \tan^{-1}(-1)\ =\ 315^\circ]


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