Question

Aratati ca sin x=12/13 tiind ca x E(0, pi/2 si cos x=5/13

Va rog sa imi explicati si mie cum se face , am nevoie de 6:50 la matematica

Answer 1

sin²x+cos²x=1
sin²x=1-cos²x
sinx=+-√(1-cos²x)
sinx=+-√(1-25/169)=+-√(169/169-25/169)=+-√144/169=+-12/13
deoarece pentru x∈(0,π/2) sinx>0, x=12/13

Answer 2

(sin x)^2 + (cos x)^2=1
(sin x)^2= 1-(cos x)^2
sin x = +/- $\sqrt{1-(cos x)^2}$
x ∈ (0, pi/2) ⇒ sin x = $\sqrt{1-(cos x)^2}$
sin x= $\sqrt{1- \frac{25}{169} }= \sqrt{ \frac{169}{169}- \frac{25}{169} }= \sqrt{ \frac{144}{169} }= \frac{12}{13}$