Question

Fie α apartine (π, 3π/2) astfel încât cos α =−5/13 . Să se calculeze sin α .

Answer 1

$a\in \Big(\pi, \dfrac{3\pi}{2}\Big), \quad \cos a= -\dfrac{5}{13}\\ \\ \sin^2 a + \cos^2 a = 1 \Rightarrow \sin ^2 a = 1-\cos^2 a \Rightarrow \\ \\ \Rightarrow \sin^2 a = 1 - \Big(-\dfrac{5}{13}\Big)^2 \Rightarrow \sin^2 a= 1-\dfrac{25}{169} \Rightarrow \\ \\ \Rightarrow \sin^2 a = \dfrac{169-25}{169} \Rightarrow \sin^2 a = \dfrac{144}{169} \Rightarrow \\ \\ \Rightarrow \sin a= \pm\sqrt{\dfrac{144}{169}} \Rightarrow \sin a = \pm\dfrac{12}{13}, ~dar,~a\in \Big(\pi, \dfrac{3\pi}{2}\Big) \Rightarrow \\ \\ \Rightarrow \boxed{\sin a = - \dfrac{12}{13}}$