Find the Exact Value cot(3)

Problem

cot(3)

Solution

1. Identify the expression as the cotangent of 3 radians.

2. Recognize that 3 is not a standard reference angle (like π/6 π/4 or π/3 for which exact algebraic values using radicals are typically derived.

3. Express the function in terms of sine and cosine using the quotient identity.

4. Conclude that since 3 is a transcendental number and not a rational multiple of π that yields a standard radical, the exact value is simply the expression itself.

Final Answer

cot(3)=cot(3)

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