Question

Вычислить cos α, tg α, ctg α, sin 2α, cos 2α, если sinα = −2/5 и π < α <3π/2

Answer 1

Ответ:

Объяснение:

$sin\alpha =-\frac{2}{5} ;\pi <\alpha <\frac{3\pi }{2};cos\alpha =?;tg\alpha =?;ctg\alpha=?;sin2\alpha =?;cos2\alpha =?.\\cos\alpha =\sqrt{1-sin^{2}\alpha } =\sqrt{1-(-\frac{2}{5})^{2} }=\sqrt{1-\frac{4}{25} } =\sqrt{\frac{21}{25} } =б\frac{\sqrt{21} }{5} .\\\pi <\alpha <\frac{3\pi }{2};cos\alpha =-\frac{\sqrt{21} }{5}.\\tg\alpha =\frac{-\frac{2}{5} }{\frac{-\sqrt{21} }{5} } =\frac{2}{\sqrt{21} } =\frac{2\sqrt{21} }{21}.\\ctg\alpha =\frac{\sqrt{21} }{2} .$

$sin2\alpha=2*sin\alpha *cos\alpha =2*(-\frac{2}{5})*(-\frac{\sqrt{21} }{5} )=\frac{4\sqrt{21} }{25} .\\ cos2\alpha =cos^{2}\alpha -sin^{2}\alpha =(-\frac{\sqrt{21} }{5})^{2} -(-\frac{2}{5})^{2} =\frac{21}{25}-\frac{4}{25} =\frac{17}{25.}$