Take into account that when you have the inverse of a fraction, say, the inverse of a/b, then, you have:
1/(a/b) = b/a
that is, the inverse of a fraction is the fraction inverted.
· csc θ = 1/sinθ
if sin θ = 12/13, then:
csc θ = 1/(12/13) = 13/12
· sec θ = 1/cosθ
if cos θ = -5/13, then:
sec θ = 1/(-5/13) = -13/5
· cot θ = 1/tanθ
if tanθ = -12/5, then:
cot θ = 1/(-12/5) = -5/12
