Find the Exact Value cos(4pi)

Problem

cos(4*π)

Solution

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

2. Simplify the angle by subtracting multiples of the period. Since 4*π is exactly 2×2*π the angle is coterminal with 0

4*π−2*(2*π)=0

3. Evaluate the cosine of the simplified angle. On the unit circle, the cosine of an angle represents the xcoordinate of the point. At 0 radians, the point is (1,0)

cos(0)=1

Final Answer

cos(4*π)=1

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