Question

Sabendo-se que sen x = 4/5, calcule o sen 2x. Lembre-se: sen^2x + cos^2x = 1

Answer 1

$\large\boxed{\begin{array}{l}\sf sen(x)=\dfrac{4}{5}\longrightarrow sen^2(x)=\dfrac{16}{25}\\\sf cos^2(x)=\dfrac{25}{25}-\dfrac{16}{25}=\dfrac{9}{25}\\\\\sf cos(x)=\sqrt{\dfrac{9}{25}}=\dfrac{3}{5}\\\\\sf sen(2x)=2\cdot sen(x)\cdot cos(x)\\\\\sf sen(2x)=2\cdot\dfrac{4}{5}\cdot\dfrac{3}{5}\\\\\Huge\boxed{\boxed{\boxed{\boxed{\sf sen(2x)=\dfrac{24}{25}}}}}\end{array}}$