Find the Exact Value tan(21pi)

Problem

tan(21*π)

Solution

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

2. Rewrite the angle 21*π in terms of the period. Since 21 is an integer, we can express the angle as 0+21*π

3. Apply the periodicity property. Using the property tan(θ+n*π)=tan(θ) we set θ=0 and n=21

tan(21*π)=tan(0)

4. Evaluate the tangent of zero. Recall that tan(0)=sin(0)/cos(0) Since sin(0)=0 and cos(0)=1 the value is 0

tan(0)=0

Final Answer

tan(21*π)=0

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