[tex]\alpha\in(90^o\,,\ 180^o)\quad\implies\quad \sin\alpha>0[/tex]
Korzystamy z jedynki trygonometrycznej:
[tex]\sin^2\alpha+\cos^2\alpha=1[/tex]
a)
[tex]\sin^2\alpha+\cos^2\alpha=1\\\\\sin^2\alpha+(-\frac45)^2=1\\\\ \sin^2\alpha+\frac{16}{25}=1\\\\\boxed{\sin^2\alpha=\frac{9}{25}}\quad\wedge\quad\sin\alpha>0 \\\\ \boxed{\sin\alpha=\frac35}[/tex]
b)
[tex]\sin^2\alpha+\cos^2\alpha=1\\\\\sin^2\alpha+(-\frac13)^2=1\\\\ \sin^2\alpha+\frac19=1\\\\\boxed{\sin^2\alpha=\frac89}\quad\wedge\quad\sin\alpha>0 \\\\ \boxed{\sin\alpha=\frac{2\sqrt2}3}[/tex]
