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

Problem

cot(−(2*π)/3)

Solution

1. Use the odd-even property of the cotangent function, which states that cot(−θ)=−cot(θ)

cot(−(2*π)/3)=−cot((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 cotangent function in the second quadrant. In Quadrant II, cotangent is negative.

cot((2*π)/3)=−cot(π/3)

4. Substitute the known value for cot(π/3) which is 1/√(,3) or √(,3)/3

cot(π/3)=√(,3)/3

5. Combine the results to find the final value.

−(−√(,3)/3)=√(,3)/3

Final Answer

cot(−(2*π)/3)=√(,3)/3

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