Find the Exact Value cos(125)

Problem

cos(125)

Solution

1. Identify the angle and the required operation. The task is to find the exact value of cos(125)

2. Determine if the angle is a standard reference angle. The angle 125 is not a standard angle (like 30 45 or 60 and cannot be expressed as a simple sum or difference of standard angles that result in a clean radical expression without nested radicals.

3. Apply the definition of the cosine function for non-standard angles. Since 125 is in the second quadrant, the value will be negative.

4. Express the value using the reference angle. The reference angle is 180−125=55

cos(125)=−cos(55)

5. Conclude that without further instructions to use specific identities (like half-angle or triple-angle formulas which would result in complex nested radicals), the exact value is represented by the trigonometric expression itself.

Final Answer

cos(125)=cos(125)

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