Define the inverse cotangent function by restricting the domain of the cotangent function to the interval (0, π). Evaluate the expression without using a calculator. (Enter your answer in radians.)

Question

arccot(− √3)

Answer 1

arccot(− √3) means you are looking for an angle θ
so that cot θ = -√3 = -√3/1
or tan θ = -1/√3

now, you should be familiar with the 30-60-90° triangle and the corresponding
side ratios of 1 : √3 : 2
that is, you should know that tan30° = 1/√3 or tan π/6 = 1/√3
but, we are told that the tangent is negative and we are restricted to 0 ≤ θ ≤ π
so θ must be in the 2nd quadrant, and θ = π-π/5 = 5π/6

arccot(− √3) = 5π/6