Question 609630
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(\phi\ +\ \theta\right)\ =\ \cos\left(\phi\right)\cos\left(\theta\right)\ -\ \sin\left(\phi\right)\sin\left(\theta\right)]


Let *[tex \LARGE \phi\ =\ 270^\circ], then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(270\ +\ \theta\right)\ =\ \cos\left(270\right)\cos\left(\theta\right)\ -\ \sin\left(270\right)\sin\left(\theta\right)]


Check the unit circle *[tex \LARGE \cos\left(270^\circ\right)\ =\ 0] and *[tex \LARGE \sin\left(270^\circ\right)\ =\ -1]


Substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(270\ +\ \theta\right)\ =\ \left(0\right)\cos\left(\theta\right)\ -\ \left(-1\right)\sin\left(\theta\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ =\ \ sin(\theta)]


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