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.)
arccot (-√3)
cot(π/6) = √3
since cot(x) is negative in QII and QIV, what do you think?
To evaluate the expression arccot(-√3), we need to find the angle in the interval (0, π) whose cotangent is -√3.
The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle. In this case, we need to find the angle whose cotangent is -√3.
Recall that the cotangent of an angle is equal to 1/tan.
Since we know that cot(π/3) = -√3, we can conclude that tan(π/3) = 1/(-√3).
Now, let's find the angle whose tangent is 1/(-√3). To do this, we can use the inverse tangent function or arctan function.
Using arctan, we have tan^(-1)(1/(-√3)) = π/6.
However, we are looking for the angle in the interval (0, π), so the final result is:
arccot(-√3) = π - (π/6) = 5π/6.
Therefore, the value of arccot(-√3) without using a calculator is 5π/6 radians.