Dados senx = 1/2 e cosx = √3/2, com 0 < x < π/2 quanto vale tgx?.... Pergunta de ideia deMegaLFRD

MegaLFRD @MegaLFRD

April 2020 1 77 Report

Dados senx = 1/2 e cosx = √3/2, com 0 < x < π/2 quanto vale tgx?

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$\\\tan\,x=\frac{\sin\,x}{\cos\,x}\\\\\tan\,x=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}\\\\\tan\,x=\frac{1}{2}\div\frac{\sqrt{3}}{2}\\\\\tan\,x=\frac{1}{2}\times\frac{2}{\sqrt{3}}\\\\\tan\,x=\frac{1}{\sqrt{3}}\;\;\times\frac{\sqrt{3}}{\sqrt{3}}\\\\\tan\,x=\frac{\sqrt{3}}{3}\\\\\boxed{x=30^o}\;\;ou\;\;\boxed{x=\frac{\pi}{6}}$

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