Question

помогите выличить (срочно нужно):
а) arccos(-cos п/4)
б) arccos(-cos 3п/4)
в) arcctg (-tg 2п/3)
г) arcsin (-sin 7/3 п)

Answer 1

а)arccos(-cos π/4)=π-arccos(cos π/4)=π-arccos(√2/2)=π-π/4=π*4 - π/4*1=4π/4-π/4=(4π-π)/4=3π/4
б)arccos(-cos 3π/4)=π-arccos(cos 3π/4)=π-arccos(cos(π-π/4))=π-arccos(cos(-π/4))=π-arccos(cos π/4)=π-arccos(√2/2)=π-π/4=3π/4
в)arcctg (-tg 2π/3)=-arcctg (tg 2π/3)=-arcctg (tg 2п/3)=-arcctg (tg(π-π/3)=-arcctg (tg(-π/3))=-arcctg (-tg π/3)=arcctg (tg π/3)=arcctg(√3)=π/3
г)arcsin (-sin 7/3 п)=-arcsin (sin 7/3 п)=-arcsin(sin(2π+π/3))=-arcsin(sinπ/3)=-arcsin(√3/2)=-π/3