Find the Exact Value tan((4pi)/3)

Problem

tan((4*π)/3)

Solution

1. Identify the quadrant of the angle (4*π)/3 Since π<(4*π)/3<(3*π)/2 the angle is in Quadrant III.

2. Determine the reference angle. For an angle θ in Quadrant III, the reference angle θ′ is calculated as θ−π

θ′=(4*π)/3−π

θ′=π/3

3. Apply the sign for the tangent function in Quadrant III. In Quadrant III, the tangent of an angle is positive.

tan((4*π)/3)=tan(π/3)

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

tan(π/3)=√(,3)

Final Answer

tan((4*π)/3)=√(,3)

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