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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