Question

Sabendo que Tg α = 1/4, calcule sen 2α

Answer 1

Resposta:

tan α =1/4

sen α/cos α =1/4

4*sen(α) =cos(α)

Sabemos que sen²(α)+cos²(α)=1

sen²(α)+ [4*sen(α)]²=1

17*sen²(α)=1  ==> sen²(α)=1/17  ==>sen(α) =±1/√17=±√17/17

Se  sen(α)  =√17/17 ==> cos(α)=4√17/17

Se  sen(α)  =-√17/17 ==> cos(α)=-4√17/17

sen(α+α)=sen(α)*cos(α)*cos(α)*sen(α) =2*sen(α)*cos(α)

sen(2α) = 2 * √17/17  * 4√17/17 = 8*17/17²=8/17

sen(2α) = 2 * (-√17/17)  * (-4√17/17) = 8*17/17²=8/17

Resposta : sen(2α) =  8/17