Question

problema 6 din poza atașată! coroana!

Answer 1

sin²α + cos²α = 1
cos²α = 1 - 4/9 = 5/9   cosα = √5 /3

Answer 2

Avem ΔABC dreptunghic in A  (<A = 90°)

sin B = b/a  = 2/3
cos B = c/a
Aplicam teorema lui Pitagora:
b² + c² = a²

$(b^{2}+c^{2} )/a^{2}=1 \\\\ b^{2}/ a^{2} +c^{2}/a^{2} =1 \\\\ c^{2}/a^{2} =1-b^{2}/ a^{2} \\\\ c/a= \sqrt{1-b^{2}/ a^{2}} \\\\ c/a= \sqrt{1-4/9} \\\\ c/a= \sqrt{5}/3 \\\\ cosB=c/a=\sqrt{5}/3$

=>  cosB = √5 / 3