Find the Exact Value cos(23)

Problem

cos(23)

Solution

1. Identify the nature of the angle 23 This angle is not a standard reference angle (such as 0 30 45 60 or 90, nor is it a simple sum or difference of standard angles that results in a basic radical expression.

2. Determine if an exact algebraic form exists. While exact values for all integer angles can be expressed using radicals (via the complex roots of unity), the expression for cos(23) involves nested cube roots and complex numbers that do not simplify into a standard radical form used in trigonometry courses.

3. Conclude that the expression cos(23) is already in its simplest exact trigonometric form.

Final Answer

cos(23)=cos(23)

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