Find the Exact Value cot(40)

Problem

cot(40^∘)

Solution

1. Identify the expression as the cotangent of 40 degrees.

2. Recognize that 40^∘ is not a standard reference angle (such as 0^∘ 30^∘ 45^∘ 60^∘ or 90^∘ for which exact values are typically expressed using simple radicals.

3. Express the value using the definition of cotangent as the ratio of cosine to sine.

cot(40^∘)=cos(40^∘)/sin(40^∘)

4. Determine if further simplification is possible. While there are complex radical expressions for angles in increments of 3^∘ 40^∘ does not result in a simple algebraic form. Therefore, the exact value is represented by the trigonometric function itself.

Final Answer

cot(40^∘)=cot(40^∘)

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