Find the Exact Value cot(25)

Problem

cot(25^∘)

Solution

1. Identify the expression as the cotangent of an angle measured in degrees, cot(25^∘)

2. Apply the identity for cotangent in terms of sine and cosine to rewrite the expression.

cot(25^∘)=cos(25^∘)/sin(25^∘)

3. Recognize that 25^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘.

4. Determine if the value can be expressed using radicals. Since 25^∘ is not a multiple of 3^∘ its trigonometric values cannot be expressed using only square roots and basic arithmetic operations (it requires cube roots via the triple-angle formula).

5. Conclude that the simplest exact form is the trigonometric expression itself.

Final Answer

cot(25^∘)=cot(25^∘)

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