Найти cosα, tgα, ctgα если sinα=5/13 и π/2<α<π

Question

Найти cosα, tgα, ctgα если sinα=5/13 и π/2<α<π

Answer 1

Sinα=5/13, α∈(π/2, π)
cosα=-√(1-sin²α)=-√(1-25/169)=-√(144/169)=-12/13
tgα=sinα/cosα=(5/13)/(-12/13)=-5/12
ctgα=1/tgα=1/(-5/12)=-12/5