Question

sa se calculeaze sin x, știind că cos x=5/13, x€(0°; 90°)

Answer 1

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Answer 2

$\text{Il calculam pe }\sin x\text{ din teorema fundamentala a trigonometriei.}\\ \boxed{\sin^2 x+\cos^2 x=1}\\ \sin^2 x=1-\cos^2 x\\ \sin^2 x=1-\dfrac{25}{169}\\ \sin^2 x=\dfrac{144}{169}\\ \\ \sin x=\pm \dfrac{12}{13}\\ \text{Dar }x\in\left(0,\dfrac{\pi}{2}\right),\text{deci e pozitiv.Prin urmare }\boxed{\sin x=\dfrac{12}{13}}$