Question

Sabendo que sen( x) = 1/5 e x ∈ [ π/2; π ] calcular cos(x).

Answer 1

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$\sf sen(x)=\dfrac{1}{5}\implies sen^2(x)=\dfrac{1}{25}\\\sf{\dfrac{25}{25}-\dfrac{1}{25}=\dfrac{24}{25}}\\\sf cos^2(x)=\dfrac{24}{25}\\\sf cos(x)=-\sqrt{\dfrac{24}{25}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf cos(x)=-\dfrac{2\sqrt{6}}{5}\checkmark}}}}$