Question

What is cot-1(2pi/3)?

Answer 1

`cot^(-1)((2pi)/3) approx 0.445`
or
`(cot((2pi)/3))^(-1) = -sqrt(3)`,
depends on the original problem statement.

Explanation:

If this means `cot^(-1)((2pi)/3)` then it's unusual to evaluate this since generally you find inverse trig functions of ratios, not angles, and `(2pi)/3` is an angle. A calculator says that `cot^(-1)((2pi)/3) approx 0.445`.

If the question actually means `(cot((2pi)/3))^(-1)` then the problem makes a little more sense.

`(cot((2pi)/3))^(-1) = 1/(cot((2pi)/3)) = tan((2pi)/3) = -sqrt(3)`.