Find the Exact Value cos(1/4)

Problem

cos(1/4)

Solution

1. Identify the expression as the cosine of a real number (radian) value.

2. Determine if the value corresponds to a standard angle on the unit circle. The value 1/4 (approximately 0.25 radians) is not a standard multiple of π (such as π/6 π/4 or π/3.

3. Conclude that since 1/4 is not a standard angle, the exact value cannot be simplified into a simpler algebraic form involving integers or square roots.

4. State the exact value in its original trigonometric form.

Final Answer

cos(1/4)=cos(1/4)

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