Question

Dado senx 3/5 calcule sen 2x e cos 2x

Answer 1

Resposta:

$\sin(2x) = \frac{24}{25} \\ \cos(2x) = \frac{7}{25}$

Explicação passo-a-passo:

Para achar cosx

${ \sin }^{2} x + \cos^{2} x = 1 \\ \sin( \frac{3}{5} )^{2} = 1 - \cos^{2} \\ \frac{9}{25} - 1 = - \cos^{2} \\ \frac{9}{25} - \frac{25}{25} = - \cos^{2} \\ - \frac{16}{25} = - \cos^{2} \\ \cos = \sqrt[2]{ \frac{16}{25 \\ \cos = \frac{4}{5}$

$\sin(2x) = 2 \times \sin(x ) \times \cos(x) \\ = 2 \times \frac{3}{5} \times \frac{4}{5} \\ = \frac{24}{25}$

$\cos(2x) = \cos^{2} - \sin^{2} \\ = {( \frac{4}{5}) }^{2} - { (\frac{3}{5}) }^{2} \\ = \frac{16 }{25} - \frac{9}{25} \\ = \frac{7}{25}$