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

Problem

sin(2*π)

Solution

1. Identify the angle on the unit circle. The angle 2*π radians represents one full counterclockwise 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 sine function on the unit circle. For any point (x,y) on the unit circle, sin(θ)=y

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

Final Answer

sin(2*π)=0

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