Question

AJUDEM!!!!!
Dado que sen x = 3/5 e que x pertence ao 2º quadrante, calcule sen 2x, cos 2x e tg 2x.

Answer 1

${\sin}^{2}(x)={(\dfrac{3}{5})}^{2}=\dfrac{9}{25}$

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

$\cos(x)=-\sqrt{\dfrac{16}{25}}=-\dfrac{4}{5}$

$\sin(2x)=2.\dfrac{3}{5}.(-\dfrac{4}{5})=-\dfrac{24}{25}$

$\cos(2x)=\dfrac{16}{25}-\dfrac{9}{25}=\dfrac{7}{25}$

$\tan(2x)=(-\dfrac{24}{25})\div\dfrac{7}{25}\\=(-\dfrac{24}{25}).\dfrac{25}{7}=-\dfrac{24}{7}$