What 2 ways are there of computing the inverse cotangent of negative square root 7?

Rachel: What 2 ways are there of computing the inverse cotangent of negative square root 7?
What caused the difference in the answers? What is the correct answer [rounded to the nearest thousandth]? Explain/show how to arrive at the correct answer using each method. [Hint – think range]. Be as specific as possible.

Answers and Views:

Answer by Seamus O
Hope this is the sort of thing your asking for:

The cotangent is related to the tangent ratio

So cot is negative whenever tan is negative

Tan is negative in the 2nd and 4th quadrants so Ө will lie in either the 2nd or 4th quadrants.

For the domain 0 ≤ Ө ≤ 360, there will be two answers found as follows:

cot Ө = -√7

1/tan Ө = -√7

tan Ө = 1/(-√7)

Ө = tan^(-1) [1/(-√7)]

Ө = 180º – 20.705º or Ө = 360º – 20.705º

Ө = 159.295º or Ө = 339.295º to the nearest thousandth of a degree

Both these answers are correct unless there is a restriction given to the domain of Ө which would exclude one of them.

If the domain has not been specified then coterminal angles should also be included.