Find the Exact Value tan(6pi)

Problem

tan(6*π)

Solution

1. Identify the period of the tangent function. The tangent function tan(θ) has a period of π meaning tan(θ+n*π)=tan(θ) for any integer n

2. Simplify the angle using the periodicity. Since 6*π is a multiple of π we can write 6*π=0+6*π

3. Apply the property tan(θ+n*π)=tan(θ)

tan(6*π)=tan(0)

4. Evaluate the tangent of 0 Recall that tan(θ)=sin(θ)/cos(θ)

tan(0)=sin(0)/cos(0)

5. Substitute the known values sin(0)=0 and cos(0)=1

tan(0)=0/1

tan(0)=0

Final Answer

tan(6*π)=0

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