Find the Exact Value cos(5/8)

Problem

cos(5/8)

Solution

1. Identify the task as finding the exact value of the cosine of a real number (in radians).

2. Determine if the value 5/8 corresponds to a standard angle on the unit circle.

3. Observe that 5/8 is not a multiple of standard angles like π/6 π/4 or π/3

4. Conclude that without a variable π in the argument, the expression cos(5/8) represents the cosine of 0.625 radians.

5. State the exact value, which is the expression itself, as it cannot be simplified into radicals or rational numbers.

Final Answer

cos(5/8)=cos(5/8)

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