Question

Sabendo que 0 < π < π/2 sen x = 3/5, determine cos x
( coloquem os cálculos por favor )

Answer 1

$\mathbf{Dados}\Longrightarrow \sin{x}=\dfrac{3}{5},\ 0<x<\dfrac{\pi}{2}.$

$\boxed{\sin^2{x}+\cos^2{x}=1}$

$\Longrightarrow\bigg(\dfrac{3}{5}\bigg)^2+\cos^2{x}=1\Longrightarrow \cos^2{x}=1-\dfrac{9}{25}$

$\Longrightarrow \cos^2{x}=\dfrac{25}{25}-\dfrac{9}{25}=\dfrac{16}{25}$

$\Longrightarrow \cos{x}=\pm\sqrt{\dfrac{16}{25}}\ \therefore\ \cos{x}=\pm\dfrac{4}{5}$

$\boxed{\cos{x}=\dfrac{4}{5}}\ \because\ 0<x<\dfrac{\pi}{2}.$