Evaluate cos(6pi)

Problem

cos(6*π)

Solution

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

2. Rewrite the angle in terms of the period. The angle 6*π can be expressed as 3×2*π

3. Apply the periodicity property. Since 6*π is an even multiple of π it is coterminal with 0

cos(6*π)=cos(0+3×2*π)

cos(6*π)=cos(0)

4. Evaluate the cosine of zero. On the unit circle, the x-coordinate at 0 radians is 1

cos(0)=1

Final Answer

cos(6*π)=1

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