Question

sin a/2=8/17; п<а<2п; найти cos a и tg a​

Answer 1

$sin\frac{a}{2} = \frac{8}{17} => cos\frac{a}{2} = -\sqrt{1 - (\frac{8}{17})^2} = -\frac{15}{17} \\cosa = cos^2\frac{a}{2} - sin^2\frac{a}{2} = \frac{161}{289}\\ tan(a) = \sqrt{\frac{1}{cos^2(a)} - 1 } = \sqrt{\frac{289^2}{161^2} - 1} = \sqrt{\frac{450*128}{161^2} } = \frac{240}{161}$