Find the Exact Value cot(68)

Problem

cot(68)

Solution

1. Identify the given expression as the cotangent of 68 degrees.

2. Recognize that 68 is not a standard angle (like 30 45 or 60, so the exact value is typically expressed in terms of trigonometric functions of that angle or its complement.

3. Apply the cofunction identity cot(θ)=tan(90−θ) to relate it to its complement.

4. Calculate the complement: 90−68=22

5. Conclude that the exact value is tan(22) or simply cot(68) as it cannot be simplified further into basic radicals without complex nested square roots.

Final Answer

cot(68)=tan(22)

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