Sinальфа = 1/2, P / 2 & lt; альфа & lt; P

Sinальфа = 1/2, P / 2<альфа <P

  •  a) \; \ sin \ alpha = \ frac12 \\\ sin ^ 2 \ alpha + \ cos ^ 2 \ alpha = 1 \ Rightarrow \ cos \ alpha = \ sqrt {1 \ sin ^ 2 \ alpha} = \ sqrt {1 \ frac14} = \ sqrt {\ frac34} = \ pm \ frac {\ sqrt3} 2 \\\ frac \ pi2 \ \ textless \ \ alpha \ \ textless \ \ pi \ Rightarrow \ cos \ alpha \ \ textless \ 0 \\\ cos \ alpha = - \ frac {\ sqrt3} 2 \\ tg \ alpha = \ frac {\ sin \ alpha} {\ cos \ alpha} = \ frac12: \ frac {\ sqrt3} 2 = \ frac12 \ cdot \ frac2 { \ sqrt3} = \ frac1 {\ sqrt3} \\\\ b) \; \ cos2 \ alpha = \ cos ^ 2 \ alpha- \ sin ^ 2 \ alpha = \ frac34- \ frac14 = \ frac24 = \ frac12