Question

Вычислите ctg(t-3П),sin (t+2П),tg(t-П),если cos(t+2П)=-1213,П<t<3П2

Answer 1

cos(t+2πn)=cost
cos(t+2π)=cost,π<t<3π/2
sint=-√(1-cos²t)=-√(1-144/169)=-√(25/169)=-5/13
1)ctg(x-πn)=ctgx
ctg(t-3π)=ctgt=cost/sint=-12/13:(-5/13)=12/13*13/5=12/5
2)sin(x+2πn)=sinx
sin(t+2π)=sint=-5/13
3)tg(x-πn)=tgx=sint/cost=-5/13:(-12/13)=5/13*13/12=5/12
tg(t-π)=tgt