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

Problem

cot((5*π)/6)

Solution

1. Identify the reference angle for (5*π)/6 by determining its distance from the nearest x-axis.

(θ_ref)=π−(5*π)/6

(θ_ref)=π/6

2. Determine the quadrant in which the angle (5*π)/6 lies. Since π/2<(5*π)/6<π the angle is in Quadrant II.

3. Recall the sign of the cotangent function in Quadrant II. In Quadrant II, x is negative and y is positive, so cot(θ)=x/y is negative.

4. Apply the cotangent value for the reference angle π/6 (or 30.

cot(π/6)=√(,3)

5. Combine the reference value with the correct sign for Quadrant II.

cot((5*π)/6)=−√(,3)

Final Answer

cot((5*π)/6)=−√(,3)

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