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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