Find the Exact Value cos(12/15)

Problem

cos(12/15)

Solution

1. Simplify the fraction inside the cosine function by dividing the numerator and the denominator by their greatest common divisor, which is 3

12/15=4/5

2. Rewrite the expression using the simplified fraction.

cos(4/5)

3. Identify that the value 4/5 is in radians and does not correspond to a standard reference angle (like π/6 or π/4.

4. Determine that since the task asks for an exact value and the angle is not a standard multiple of π the expression cannot be simplified further into a radical or integer form.

Final Answer

cos(12/15)=cos(4/5)

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