Réponses

2014-01-07T00:12:02+01:00
Bonsoir,

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

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\\\\

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}

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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}