Find the Exact Value tan(-(2pi)/3)

Problem

tan(−(2*π)/3)

Solution

1. Use the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−(2*π)/3)=−tan((2*π)/3)

2. Identify the reference angle for (2*π)/3 Since the angle is in the second quadrant, the reference angle is π−(2*π)/3=π/3

Reference Angle=π/3

3. Determine the sign of the tangent function in the second quadrant. In Quadrant II, tangent is negative.

tan((2*π)/3)=−tan(π/3)

4. Substitute the known value for tan(π/3) which is √(,3)

tan((2*π)/3)=−√(,3)

5. Combine the results by substituting this back into the expression from step 1.

−tan((2*π)/3)=−(−√(,3))

6. Simplify the signs to find the final value.

−(−√(,3))=√(,3)

Final Answer

tan(−(2*π)/3)=√(,3)

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