Question

sendo cosx= 5m-9 calcule o valor de "m" que satisfaz a equação
Me ajude, por favor

Answer 1

O $\mathsf{cos (x)}$ está definido entre 1 e -1. Assim:

$\mathsf{-1\le cos\left(x\right)\le 1}\\\mathsf{-1\le 5m-9\le 1}\\\mathsf{9-1\le 5m-9+9\le 1+9}\\\mathsf{8\le 5m\le 10}\\\\\mathsf{\dfrac{8}{5}\le \dfrac{5m}{5}\le \dfrac{10}{5}}\\\\\mathsf{\dfrac{8}{5}\le m\le 2}\\\\\\\boxed{\mathsf{S=\left\{m\in \mathbb{R}\:/\:\dfrac{8}{5}\le \:\:m\le \:\:2\right\}}}$