Question

Помогите решить $1) cos(\pi -\alpha ) esli sina=\frac{8}{17} \\2) sin(\pi -\alpha ) esli\\ cosa=\frac{15}{17}$

Answer 1

Ответ:

Объяснение:

$cos(\pi -\alpha)=-cos\alpha ; sin\alpha =\frac{8}{17} \\-cos\alpha=-\sqrt{1-sin^{2}\alpha } =-\sqrt{1-(\frac{8}{17} )^{2} }=-\sqrt{1-(\frac{8}{17} )^{2} }=-\frac{\sqrt{289-64}}{17} =-\frac{\sqrt{225}}{17} =-\frac{15}{17}$

$sin(\pi -\alpha )=sin\alpha ; cos\alpha =\frac{15}{17} ;\\sin\alpha=\sqrt{1-cos^{2}\alpha } =\sqrt{1-(\frac{15}{17}) ^{2} }=\frac{\sqrt{289-225} }{17} =\frac{\sqrt{64} }{17} =\frac{8}{17}$