Final answer:
To evaluate cot 112°5', find the tangent of the angle and then take its reciprocal. In the second quadrant, the tangent is negative.
Step-by-step explanation:
To evaluate the value of cot 112°5', we need to find the cotangent of this angle. The cotangent ratio is the reciprocal of the tangent ratio. So, cot 112°5' = 1/tan 112°5'. To find the value of the tangent, we can use the unit circle.
The angle 112°5' falls in the second quadrant. The reference angle for this angle is 180° - 112°5' = 67°55'. In the second quadrant, the tangent is negative. So, tan 112°5' = -tan 67°55'.
Using a calculator or trigonometric table, we find that tan 67°55' is approximately 2.5. Therefore, cot 112°5' ≈ 1/2.5 ≈ 0.4.