1) а) = Cos90° = 0
б) = Sin60° = √3/2
в) = Сos(7π/12 + 5π/12) = Cosπ = -1
г) = Сos4α
2) а) = Sinα
б) = -Cosα
в) = -tgα
г) = 0
д) Sin(π/4 -α ) = Sinπ/4Cosα - Cosπ/4Sinα = √2/2Cosα - √2/2Sinα =
=√2/2(Сosα - Sinα)
Sinα = -0,8. ищем Cosα
Cos²α = 1 - Sin²α = 1 - 0,64 = 0,36, ⇒ Cosα = 0,6
наш пример:
√2/2(Сosα - Sinα) = √2/2(0,6 +0,8) = √2/2*1,4 =0,7√2
3) а) = Cos(2π+π/6) = Cosπ/6 = √3/3
б) =Sin240° = Sin(270° -30°) = -Cos30° = -√3/2
в) 8Sin(-150°)*Cos120°*Ctg210°*tg240°=
-8Sin150°*Cos(180° - 60 °)*Ctg(270°-60°) * tg(270°-30°)=
=-8*Sin(180 -30)*(-Cos60)*tg60*Ctg30=8Sin30*Cos60°*tg60°*Ctg30°=
=8*1/2*1/2*√3*√3 = 12
г) 2tg6°Ctg84°-Ctg(-450°) = 2tg6°*tg6° + 0 = 2tg² 6°