Find the Exact Value tan((7pi)/3)

Problem

tan((7*π)/3)

Solution

1. Identify the angle and determine its position relative to a full rotation of 2*π radians.

2. Subtract 2*π from the angle to find its coterminal equivalent within the interval [0,2*π)

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

3. Apply the property of periodic functions, noting that tan(θ)=tan(θ−2*π)

tan((7*π)/3)=tan(π/3)

4. Evaluate the tangent of the reference angle π/3 using known trigonometric values.

tan(π/3)=√(,3)

Final Answer

tan((7*π)/3)=√(,3)

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