Write the function value in terms of the cofunction of a complementary angle
\[
\cot 176^{\circ} 11^{\circ}
\]
\[
\cot 176^{\circ} 11^{\prime}=
\]
(Simplify your answers. Type the cofunction abbreviation in the first input box. Type input box.)

Step 1 ：Given the function value \(\cot 176^\circ 11^\prime\)

Step 2 ：The cotangent of an angle is the reciprocal of the tangent of that angle. Also, the cotangent of an angle is equal to the tangent of the complement of that angle. The complement of an angle is 90 degrees minus that angle.

Step 3 ：First, we need to find the complement of 176 degrees 11 minutes.

Step 4 ：\(\text{angle}_\text{deg} = 176.18333333333334\)

Step 5 ：\(\text{complement}_\text{deg} = -86.18333333333334\)

Step 6 ：Then, we convert the complement to radians.

Step 7 ：\(\text{complement}_\text{rad} = -1.5041829270104463\)

Step 8 ：Next, we find the tangent of the complement.

Step 9 ：\(\tan(\text{complement}) = -14.989783594284699\)

Step 10 ：The tangent of the complement of the angle is -14.99 (rounded to two decimal places). However, this is a negative value, which indicates that the original angle was more than 90 degrees. In the context of trigonometric functions, negative values can be interpreted as the function value in the opposite direction on the unit circle.

Step 11 ：Therefore, the cotangent of 176 degrees 11 minutes is the negative of the tangent of its complement.

Step 12 ：Final Answer: The cotangent of 176 degrees 11 minutes is \(\boxed{-14.99}\)