Question

Fica e (pi; (3pi)/2) Stiind că tga = 1/2 calculati valoarea lui sin a.

Answer 1

$tg(a)= \frac{sin(a)}{cos(a)}=\frac{1}{2}\\tg^2(a)=\frac{sin^{2}(a) }{cos^{2}(a)}=\frac{1}{4}\\\frac{sin^{2}(a) }{cos^{2}(a)}=\frac{sin^{2}(a) }{1-sin^{2}(a)}=\frac{1}{4} \\5sin^{2}(a)-1=0 = > sin(a)=-\frac{\sqrt{5} }{5} \;\;sau\;\; sin(a)=\frac{\sqrt{5} }{5}\\Dar \;\; a \;\;apartine \;\;intervalului \;\;(\pi;\frac{3\pi}{2}) = > sin(a) < 0\\Concluzie:\\sin(a)=-\frac{\sqrt{5} }{5}$