Question

Considere α um ângulo qualquer menor que 90°. Sabendo que cos α = 2/5. Calcule: Sen α

Answer 1

$seno {}^{2} ( \alpha ) + cosseno {}^{2} ( \alpha ) = 1 \\ \\ seno {}^{2} ( \alpha ) + (\frac{2}{5} ) {}^{2} = 1 \\ \\ seno {}^{2}( \alpha ) + \frac{4}{25} = 1 \\ \\ seno {}^{2}( \alpha ) = 1 - \frac{4}{25} \\ \\ seno {}^{2} ( \alpha ) = \frac{25}{25} - \frac{4}{25} \\ \\ seno {}^{2} ( \alpha ) = \frac{21}{25} \\ \\ \sqrt{ {seno}^{2} } ( \alpha ) =± \sqrt{ \frac{21}{25} } \\ \\ seno( \alpha ) = ± \frac{ \sqrt{21} }{ \sqrt{25} } \\ \\ seno( \alpha ) = ± \frac{ \sqrt{21} }{5}$