Question

sa se determine sin alfa,daca se stie ca tg alfa =5/12 si alfa apartine (π;3 π/2)

Answer 1

$1+ tg^2 \alpha = \frac{1}{cos^2 \alpha } \\ 1+( \frac{5}{12})^2= \frac{1}{cos^2 \alpha } \\ 1+ \frac{25}{144}= \frac{1}{cos^2 \alpha } \\ \frac{169}{144}= \frac{1}{cos^2 \alpha } \\ cos \alpha =- \frac{12}{13} \\ sin \alpha =- \sqrt{1- \frac{144}{169} }=- \frac{5}{13}$