Find the Exact Value cos((25pi)/3)

Problem

cos((25*π)/3)

Solution

1. Identify the periodicity of the cosine function, which is 2*π

2. Divide the numerator by the denominator to express the fraction as a mixed number or to find the number of full rotations.

(25*π)/3=8*π+π/3

3. Subtract the full rotations of 2*π to find the coterminal angle within the interval [0,2*π)

8*π=4*(2*π)

(25*π)/3−8*π=π/3

4. Evaluate the cosine of the coterminal angle using the unit circle or special triangles.

cos(π/3)=1/2

Final Answer

cos((25*π)/3)=1/2

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