Find the Exact Value tan(7pi)

Problem

tan(7*π)

Solution

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

2. Rewrite the expression by expressing 7*π in terms of the period. Since 7 is an integer, we can write 7*π as 0+7*π

3. Apply the property of periodicity where tan(θ+n*π)=tan(θ) In this case, θ=0 and n=7

4. Evaluate the resulting expression. We know that tan(0)=sin(0)/cos(0)

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

Final Answer

tan(7*π)=0

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