[tex]a\:\in\:(\pi, \frac{3\pi}{2} ) = cadranul\: III[/tex]
[tex]cos \: a = - \frac{3}{5} [/tex]
[tex] {sin}^{2} a + {cos}^{2} a = 1[/tex]
[tex] {sin}^{2} a + {( - \frac{3}{5}) }^{2} = 1[/tex]
[tex] {sin}^{2} a + \frac{9}{25} = 1[/tex]
[tex] {sin}^{2} a = 1 - \frac{9}{25} [/tex]
[tex] {sin}^{2} a = \frac{16}{25} [/tex]
[tex]sin \: a = \pm \: \sqrt{ \frac{16}{25} } [/tex]
[tex]sin \: a = \pm \: \frac{4}{5} [/tex]
[tex]a\:\in\:(\pi, \frac{3\pi}{2} ) = > sin \: a < 0 = > sin \: a = - \frac{4}{5} [/tex]
[tex]sin \: 2a = 2sinacosa[/tex]
[tex]sin \: 2a = 2sinacosa = 2 \times (- \frac{3}{5} ) \times ( - \frac{4}{5} ) = \frac{24}{25} [/tex]
