Find the Exact Value tan(12pi)

Problem

tan(12*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. Apply the periodicity to the given expression. Since 12*π is a multiple of the period π we can write 12*π as 0+12*π

3. Simplify the expression using the property tan(n*π)=tan(0) for any integer n

tan(12*π)=tan(0)

4. Evaluate the tangent of 0 using the definition 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=0

Final Answer

tan(12*π)=0

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