Find the Exact Value cot(-(5pi)/6)

Problem

cot(−(5*π)/6)

Solution

1. Apply the odd function property of the cotangent function, which states cot(−θ)=−cot(θ)

−cot((5*π)/6)

2. Identify the reference angle for (5*π)/6 Since the angle is in the second quadrant, the reference angle is π−(5*π)/6=π/6

π/6

3. Determine the sign of the cotangent function in the second quadrant. Since cot(θ)=cos(θ)/sin(θ) and cosine is negative while sine is positive in the second quadrant, the cotangent is negative.

cot((5*π)/6)=−cot(π/6)

4. Substitute the known value for cot(π/6) which is √(,3)

−cot((5*π)/6)=−(−√(,3))

5. Simplify the expression to find the final result.

√(,3)

Final Answer

cot(−(5*π)/6)=√(,3)

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