Question

exact value of

cot[arccos(-2/3)]

Answer 1

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)