Question

A medida de um angulo agudo tal que sen ALFA tal que sen alfa = 12/13 calcule cos alfa e tg alfa

Answer 1

Podemos utilizar a fórmula para descobrir o cos:

$\boxed{sen^{2}\alpha+cos^{2}\alpha = 1}$

Substituindo:

$sen^{2}\alpha+cos^{2}\alpha = 1 \\\\ (\frac{12}{13})^{2}+cos^{2}\alpha =1 \\\\ \frac{144}{169}+cos^{2}\alpha = 1 \\\\ cos^{2}\alhpa = 1-\frac{144}{169} \\\\ cos^{2}\alpha = \frac{169-144}{169} \\\\\ cos^{2}\alpha = \frac{25}{169} \\\\ cos\alpha = \pm \sqrt{\frac{25}{169}} \\\\ cos\alpha = \pm \frac{5}{13} \\\\ \boxed{angulo \ agudo < 90\°} \\\\ \boxed{\boxed{cos\alhpa = +\frac{5}{13}}}$


E tg é apenas sen sobre cos:

$tg\alpha = \frac{sen\alpha}{cos\alpha} \\\\ tg\alpha = \frac{\frac{12}{13}}{\frac{5}{13}} \\\\ tg\alpha = \frac{12 \cdot 13}{13 \cdot 5} \\\\ \boxed{\boxed{tg\alpha = \frac{156}{65}}}$