Question

1. Sa se calculeze sin x , stiind ca cos x =5/13 , x€ (0.90°) .

Answer 1

[tex]\text{Il putem afla pe cos x din teorema fundamentala a trigonometriei.}\\ \boxed{\sin^2 x+\cos ^2x=1}\\ \sin^2x+\dfrac{25}{169}=1\\ \sin^2 x=1-\dfrac{25}{169}\\ \sin^2 x=\dfrac{144}{169}\\ \sin x=\pm \dfrac{12}{13}\\ x\in \left(0\textdegree,90\textdegree\right)\Rightarrow \sin x=\dfrac{12}{13}[/tex]