Question

determine o valor de cos x sabendo que 2 sen x + 3 cos x = 0​

Answer 1

Explicação passo-a-passo:

$2sen x + 3cos x = 0 \\ 2tg x + 3 = 0 \\ 2tg x = - 3 \\ tg x = - \frac{3}{2} \\\\ tg^2 x + 1 = \frac{1}{cos^2 x} \\\\ (\frac{3}{2})^2 + 1 = \frac{1}{cos^2 x} \\\\ \frac{9}{4} + 1 = \frac{1}{cos^2 x} \\\\ \frac{13}{4} = \frac{1}{cos^2 x} \\\\ 13cos^2 x = 4 \\ cos^2 x = \frac{4}{13} \\\\ cos x = \pm \sqrt{\frac{4}{13}} \\\\ cos x = \pm \frac{2\sqrt{13}}{13}$

Espero ter ajudado.