Find the Exact Value tan(15pi)

Problem

tan(15*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 expression using the periodicity property. Since 15*π is a multiple of π we can express it as 0+15*π

3. Apply the property tan(θ+n*π)=tan(θ) where θ=0 and n=15

tan(15*π)=tan(0)

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

tan(0)=0/1

tan(0)=0

Final Answer

tan(15*π)=0

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