Find the Exact Value cot((8pi)/3)

Problem

cot((8*π)/3)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(8*π)/3−2*π=(8*π)/3−(6*π)/3

(8*π)/3−(6*π)/3=(2*π)/3

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

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

(θ_R)=π−(2*π)/3

(θ_R)=π/3

4. Apply the trigonometric identity for cotangent, noting that cotangent is negative in Quadrant II.

cot((2*π)/3)=−cot(π/3)

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

cot((2*π)/3)=−√(,3)/3

Final Answer

cot((8*π)/3)=−√(,3)/3

Want more problems? Check here!