Question

Dado que senx = 12/13, conclui-se que o valor numérico de cos 2x é:

Answer 1

$Sen^2x + Cos^2x = 1 \\ \\ (\frac{12}{13})^2 + Cos^2x = 1 \\ \\ \frac{144}{169} + Cos^2x = 1 \\ Cos^2x = 1 - \frac{144}{169} \\ \\ Cos^2x = \frac{169 - 144}{169} \\ \\ Cosx = \sqrt{\frac{25}{169}} \\ \\ Cosx = \frac{5}{13}$

Logo:

$Cos(2x) = 2cos^2x - 1 \\ Cos(2x) = 2( \frac{5}{13})^2 - 1 \\ \\ Cos(2x) = 2(\frac{25}{169}) - 1 \\ \\ Cos(2x) = \frac{50}{169} - 1 \\ \\ Cos(2x) = \frac{50 - 169}{169} = \frac{-119}{169}$