Find the Exact Value tan(9pi)

Problem

tan(9*π)

Solution

1. Identify the period 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. Apply the periodicity to the given expression. Since 9*π is an integer multiple of the period π we can write 9*π as 0+9*π

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

tan(9*π)=tan(0)

4. Evaluate the tangent of zero. Since tan(θ)=sin(θ)/cos(θ) we have:

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

tan(0)=0/1

tan(0)=0

Final Answer

tan(9*π)=0

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