Besoin d'aide svp!! si un angle aigu  tel que sinusÂ= 0,25 , Calculer Cosinus  et tangente Â

Bonsoir,

Puisque l'angle A est aigu, sin(A) > 0 ; cos(A) > 0 , tan(A) > 0.

[tex]sin(\widehat{A})=\dfrac{1}{4}\\\\sin^2(\widehat{A})+cos^2(\widehat{A})=1\\\\(\dfrac{1}{4})^2+cos^2(\widehat{A})=1\\\\\dfrac{1}{16}+cos^2(\widehat{A})=1\\\\[/tex]

[tex]cos^2(\widehat{A})=1-\dfrac{1}{16}\\\\cos^2(\widehat{A})=\dfrac{15}{16}\\\\cos(\widehat{A})=\sqrt{\dfrac{15}{16}}\\\\cos(\widehat{A})=\dfrac{\sqrt{15}}{4}[/tex]

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[tex]tan(\widehat{A})=\dfrac{sin(\widehat{A})}{cos(\widehat{A})}\\\\tan(\widehat{A})=\dfrac{\dfrac{1}{4}}{\dfrac{\sqrt{15}}{4}}\\\\tan(\widehat{A})=\dfrac{1}{4}\times\dfrac{4}{\sqrt{15}}}\\\\tan(\widehat{A})=\dfrac{1}{\sqrt{15}}}\\\\tan(\widehat{A})=\dfrac{1\times\sqrt{15}}{\sqrt{15}\times\sqrt{15}}}\\\\tan(\widehat{A})=\dfrac{\sqrt{15}}{15}[/tex]