Question

Qual a solução da equação, em IR:
cos(x + π/4) = -√ 2/2

Answer 1

$cos(x+\frac{\pi}{4}) = \frac{-\sqrt{2}}{2}\\\\\\\textsf{Sabemos que o cosseno de 135 e 225 graus vale -raiz de 2, sobre dois.}\\\\\textsf{Logo, calcularemos x de modo que se iguale a esses arcos congruos de 45.}\\\\\\x + \frac{\pi}{4} = \pi - \frac{\pi}{4}\rightarrow x = \frac{\pi}{2} + 2.k.\pi\\\\x +\frac{\pi}{4} =\pi + \frac{\pi}{4} \rightarrow x = \pi + 2.k.pi\\\\\\\boxed{S = \{x\in\mathbb{R}~|~x = \frac{\pi}{2} + 2.k.\pi ~ou~ x = \pi + 2.k.\pi~com~k\in\mathbb{Z}\}}$