trigonometry
posted by sam .
exact value of
cot[arccos(2/3)]

cos(θ)=2/3
So θ is in the second or third quadrant. There is not enough information to be sure of which.
adjacent = 2
hypotenuse = 3
opposite = ±√(3²(2)²)
= ±√(5)
Therefore
cot(θ)
=adjacent/opposite
=2/(±√(5))
= ±(2/√(5))
=±(2√(5)/5)