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

Problem

tan(2*π)

Solution

1. Identify the angle on the unit circle. The angle 2*π radians is coterminal with 0 radians, located on the positive x-axis.

2. Determine the coordinates (x,y) at this angle. On the unit circle, the point corresponding to 2*π is (1,0)

3. Apply the formula for the tangent function in terms of unit circle coordinates, which is tan(θ)=y/x

4. Substitute the values x=1 and y=0 into the formula.

5. Simplify the resulting fraction.

Final Answer

tan(2*π)=0

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