Question

Se cos x = - 1/7. Determine sen x
(COLOQUEM OS CÁLCULOS POR FAVOR)

Answer 1

$\displaystyle \underline{\text{Usando a rela{\c c}{\~a}o fundamental da trigonometria}}: \\\\ \text{sen}^2\text x+\text{cos}^2\text x = 1 \\\\ \text{sen x} =\pm\sqrt{1-\text{cos}^2\text x} \\\\ \underline{\text{substituindo o valor do cosseno}}: \\\\ \text{sen x} =\pm\sqrt{1- \frac{1}{49} } \\\\\\ \text{sen x} = \pm\sqrt{\frac{49-1}{49}} \\\\\\ \text{sen x} = \pm\frac{\sqrt{16.3}}{7}\\\\\\ \text{sen x} = \pm\frac{4\sqrt{3}}{7}$

Portanto os possíveis valores de x são :

$\huge\boxed{\ \text{sen x} = \frac{4\sqrt3}{7} \ \ ; \ \ \text{sen x} = \frac{-4\sqrt3}{7}\ }$