Question

Fie a∈(π, 3π\2),astfel incat cos a= - 3\5.Atunci sin2x este egal cu....

Answer 1

$a\:\in\:(\pi, \frac{3\pi}{2} ) = cadranul\: III$

$cos \: a = - \frac{3}{5}$

${sin}^{2} a + {cos}^{2} a = 1$

${sin}^{2} a + {( - \frac{3}{5}) }^{2} = 1$

${sin}^{2} a + \frac{9}{25} = 1$

${sin}^{2} a = 1 - \frac{9}{25}$

${sin}^{2} a = \frac{16}{25}$

$sin \: a = \pm \: \sqrt{ \frac{16}{25} }$

$sin \: a = \pm \: \frac{4}{5}$

$a\:\in\:(\pi, \frac{3\pi}{2} ) = > sin \: a < 0 = > sin \: a = - \frac{4}{5}$

$sin \: 2a = 2sinacosa$

$sin \: 2a = 2sinacosa = 2 \times (- \frac{3}{5} ) \times ( - \frac{4}{5} ) = \frac{24}{25}$