Find the Exact Value tan(5pi)

Problem

tan(5*π)

Solution

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

2. Apply the periodicity property to the given angle. Since 5*π is a multiple of π we can write 5*π as 0+5*π

3. Simplify the expression using the property tan(x+5*π)=tan(x)

tan(5*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

tan(0)=0

Final Answer

tan(5*π)=0

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