Find the Exact Value cot((11pi)/3)

Problem

cot((11*π)/3)

Solution

1. Find the coterminal angle within the interval [0,2*π) by subtracting 2*π from the given angle.

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(5*π)/3

2. Identify the quadrant for the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle is in Quadrant IV.

3. Determine the reference angle (θ_R) for an angle in Quadrant IV using the formula (θ_R)=2*π−θ

(θ_R)=2*π−(5*π)/3

(θ_R)=π/3

4. Apply the trigonometric identity for cotangent, noting that cot(θ) is negative in Quadrant IV.

cot((11*π)/3)=−cot(π/3)

5. Evaluate the exact value using the known value cot(π/3)=√(,3)/3

cot((11*π)/3)=−√(,3)/3

Final Answer

cot((11*π)/3)=−√(,3)/3

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