Final answer:
The exact value of arccot(1) is π/4 radians, as this is the angle whose cotangent is 1, corresponding to a 45-degree angle in a right triangle with equal-length legs.
Step-by-step explanation:
To find the exact value of arccot(1), we need to determine the angle whose cotangent is 1. The cotangent function is the reciprocal of the tangent function, meaning cot(θ) = 1/tan(θ). An angle with a cotangent of 1 is an angle where the tangent has the same value, namely 1. Remember that the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
In a right triangle where the sides are of equal length, the tangent of one of the non-right angles is 1, since both the opposite side and the adjacent side are the same length. This is true for a 45-degree angle (or π/4 radians). Therefore, the exact value of arccot(1) is π/4, which corresponds to option (a).