[tex] x \in \left( 0, \dfrac{\pi}{2}\right) , cos x = \dfrac{1}{4} [/tex]
Folosim formula fundamentală a trigonometriei.
[tex] \sin ^2 x + \cos ^2 x =1 \\ \sin ^2 x + \left( \dfrac{1}{4} \right)^2 =1 \\ \sin ^2 x+ \dfrac{1}{16} = 1 \\ \sin ^2 x = \dfrac{15}{16} \\ \implies \sin x = \pm \sqrt{\dfrac{15}{16}} \\ \begin{cases} \sin x = \pm \dfrac{\sqrt{15}}{4} \\ x \in \left( 0, \dfrac{\pi}{2} \right) \end{cases} \implies \tt sin x = \dfrac{\sqrt{15}}{4} [/tex]
