Find the Exact Value cos(6pi)

Problem

cos(6*π)

Solution

1. Identify the period of the cosine function. The cosine function has a period of 2*π meaning cos(θ)=cos(θ+2*π*n) for any integer n

2. Determine the number of full rotations. Since 6*π=3×(2*π) the angle 6*π represents three full rotations around the unit circle.

3. Simplify the angle using coterminal angles. The angle 6*π is coterminal with 0 because 6*π−3*(2*π)=0

4. Evaluate the cosine at the simplified angle. The value of cos(0) is 1

Final Answer

cos(6*π)=1

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