Find the Exact Value cos(26)

Problem

cos(26^∘)

Solution

1. Identify the task as finding the exact trigonometric value of cos(26^∘)

2. Determine if the angle 26^∘ is a standard reference angle (such as 0^∘,30^∘,45^∘,60^∘,90^∘ or a multiple/sum of these that yields a simple radical form.

3. Analyze the angle 26^∘ This angle is not a standard reference angle, nor can it be expressed as a simple sum or difference of standard angles (like 15^∘=45^∘−30^∘ to produce a standard exact radical form.

4. Conclude that while the value can be expressed using complex radical nested formulas involving the roots of high-degree polynomials, it does not have a simplified "exact value" in the conventional sense used in trigonometry courses. Therefore, the expression is already in its simplest exact form.

Final Answer

cos(26^∘)=cos(26^∘)

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