Evaluate tan(2pi)

Problem

tan(2*π)

Solution

1. Identify the angle on the unit circle. The angle 2*π radians is equivalent to 360 which corresponds to the point (1,0) on the unit circle.

2. Apply the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

3. Substitute the values for sin(2*π) and cos(2*π) At the point (1,0) the y-coordinate is sin(2*π)=0 and the x-coordinate is cos(2*π)=1

tan(2*π)=0/1

4. Simplify the fraction to find the final value.

tan(2*π)=0

Final Answer

tan(2*π)=0

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