Question

Calculati ctg a , stiind ca sin a = 1/3 si a apartine primului cadran .

Answer 1

[tex]\text{Mai intai sa-l calculam si pe cos a:}\\ \sin^2a+\cos^2 a=1\\ \cos^2 a=1-\sin^2 a\\ \cos ^2 a=1-\dfrac{1}{9}\\ \cos^2 a=\dfrac{8}{9}\\ \cos a=\pm \dfrac{2\sqrt 2}{3}\\ a\in \left(0,\dfrac{\pi}{2}\right)\Rightarrow \cos a=\dfrac{2\sqrt 2}{3}[/tex]
$ctg\ a=\dfrac{\cos a}{\sin a}=\dfrac{\frac{2\sqrt 2}{3}}{\frac{1}{3}}= \boxed{2\sqrt 2}$