Question

Чему равен cos a, если sin a/2=1/4

Answer 1

$cosa=cos^2 frac{a}{2}-sin^2 frac{a}{2}=1-2sin^{2} frac{a}{2}=1-2( frac{1}{4})^2=1-2* frac{1}{16}= frac{7}{8}$

Answer 2

$cosa=cos^{2} frac{a}{2} -sin ^{2} frac{a}{2} \ cos frac{a}{2} = sqrt{1- frac{1}{16} } = frac{ sqrt{15} }{4} \ cosa= frac{15}{16} - frac{1}{16} = frac{15-1}{16} = frac{14}{16} = frac{7}{8} =0.875$