Simplify cos(2pi)

Problem

cos(2*π)

Solution

1. Identify the angle on the unit circle. The angle 2*π radians represents one full revolution around the circle, ending at the same position as 0 radians.

2. Determine the coordinates of the point on the unit circle at this angle. The point corresponding to 2*π is (1,0)

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

4. Evaluate the expression using the x-coordinate of the point. Since the x-coordinate is 1 the value of the cosine is 1

Final Answer

cos(2*π)=1

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