Question

Resolva a expressão:

4.sen² x - 1 = 0

( ) 225°
( ) 60°
( ) 120°
( ) 150°

Answer 1

$\displaystyle 4\text{sen}^2(\text x)-1 = 0 \\\\ 4\text{sen}^2(\text x) = 1 \\\\ \text{sen}^2(\text x) = \frac{1}{4} \\\\ \text{sen(x)}= \pm \sqrt{\frac{1}{4}} \\\\\\ \text{sen(x)} = \frac{1}{2} \ \ \text{ou} \ \ \text{sen(x)} = \frac{-1}{2}$

Vamos analisar :

$\displaystyle \text{sen(x)} = \frac{1}{2} \\\\\text x = \{30^\circ+ 2\text k.\pi \ ,\ 150^\circ+2\text k.\pi \ \} \ \boxed{\text{com k } \in \mathbb{Z}}$

Portanto :

$\huge\boxed{\text x = 150^\circ}\checkmark$