Question

Daca tg(x) =1/3, calculati sin(x) si cos(x).

Answer 1

$tg \ x= \frac{1}{3} \\ cos \ x-? \\ sin \ x -? \\ 1+tg^2 \ x= \frac{1}{cos^2 \ x} =1+ (\frac{1}{3} )^2= \frac{9}{9} + \frac{1}{9} = \frac{10}{9} \\ cos^2 \ x \cdot 10=9 \\ \Rightarrow \boxed {cos \ x= \sqrt{ \frac{9}{10} } = \frac{3}{ \sqrt{10} } }}; \\ \frac{sin \ x}{cos \ x} =tg \ x= \frac{sin \ x}{ \frac{3}{ \sqrt{10} } } = \frac{1}{3} \\ 3sin \ x=1 \cdot \frac{3}{ \sqrt{10} } = \frac{3}{ \sqrt{10} } \\ sin \ x= \frac{3}{ \sqrt{10} } :3 \\ \Rightarrow \boxed{sin \ x= \frac{1}{ \sqrt{10} } }$