Find the Value Using the Unit Circle cos(2pi)

Problem

cos(2*π)

Solution

1. Identify the angle on the unit circle. The angle 2*π radians represents one full counter-clockwise revolution around the circle.

2. Determine the coordinates of the point on the unit circle corresponding to 2*π This point is located on the positive x-axis at (1,0)

3. Apply the definition of the cosine function on the unit circle. For any point (x,y) on the unit circle, cos(θ)=x

4. Extract the x-coordinate from the point (1,0)

Final Answer

cos(2*π)=1

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