Question

se da cosx=1/3,xe(0,90°) calculati sinx,tyx,ctgx
URGEEEENT !!!!!​

Answer 1

Explicație pas cu pas:

$\cos(x) = \frac{1}{3} ; \: x \in \left(0 ; \frac{\pi}{2} \right)$

$\sin^{2} (x) + \cos^{2} (x) = 1$

$\sin^{2} (x) = 1 - \left(\frac{1}{3} \right)^{2} = 1 - \frac{1}{9} = \frac{8}{9} \\ = > \sin(x) = \frac{2 \sqrt{2} }{3}$

$\tg(x) = \frac{ \sin(x) }{ \cos(x) } = \frac{ \frac{2 \sqrt{2} }{3} }{ \frac{1}{3} } \\ = > \tg(x) = 2 \sqrt{2}$

$\ctg(x) = \frac{ \cos(x) }{ \sin(x) } = \frac{ \frac{1}{3} }{ \frac{2 \sqrt{2} }{3} } = \frac{1}{2 \sqrt{2} } \\ = > \ctg(x) = \frac{ \sqrt{2} }{4}$