Question

Sabendo que seno a = 1/6 calcule sen 2a

Answer 1

Resposta:

-2sen\ a\ cos\ a+cos^2a=\frac{4}{25}\\\\ \boxed{sen^2a+cos^2a=1}\\\\ \boxed{sen2\ a=2sen\ a\ c

\begin{gathered}sen\ a-cos\ a=\frac{2}{5}\\\\ (sen\ a-cos\ a)^2=(\frac{2}{5})^2\\\\ sen^2aos\ a}\\\\ 1-sen2\ a=\frac{4}{25}\end{gathered}

sen a−cos a=

5

2

(sen a−cos a)

2

=(

5

2

)

2

sen

2

a−2sen a cos a+cos

2

a=

25

4

sen

2

a+cos

2

a=1

sen2 a=2sen a cos a

1−sen2 a=

25

4

\begin{gathered}sen\ 2a = 1-\frac{4}{25}\\\\ sen\ 2a=\frac{25}{25}-\frac{4}{25}\\\\ \boxed{\boxed{sen\ 2a=\frac{21}{25}}}\end{gathered}

sen 2a=1−

25

4

sen 2a=

25

25

−

25

4

sen 2a=

25

21