Question

3) (UFAM) Dada a equação senx = 2m - 9. Quais são os valores reais de m para que a equação tenha solução?​

Answer 1

$\displaystyle \text {sen x} = 2\text m-9 \\\\ \underline{\text{por{\'e}m}}: \\\\ -1\leq \text {sen x}\leq 1 \\\\ \underline{\text{Da{\'i}}}: \\\\ -1\leq 2\text m-9 \leq 1 \\\\ 2\text m-9\leq 1\to 2\text m \leq 10 \to \text m \leq 5\\\\ -1\leq 2\text m-9 \to 8\leq 2\text m \to \text m \geq 4\\\\ \underline{\text{Portanto}}:\\\\ \huge\boxed{\text S=\{\ \text m \in \mathbb{R} \ | \ 4\leq \text m \leq 5\ \}\ }\checkmark$