Find the Exact Value cot(-(4pi)/3)

Problem

cot(−(4*π)/3)

Solution

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

cot(−(4*π)/3)=−cot((4*π)/3)

2. Identify the reference angle for (4*π)/3 Since (4*π)/3 is in the third quadrant (between π and (3*π)/2, the reference angle is (4*π)/3−π=π/3

(θ_ref)=π/3

3. Determine the sign of the cotangent function in the third quadrant. In the third quadrant, cotangent is positive.

cot((4*π)/3)=cot(π/3)

4. Evaluate the cotangent of the reference angle using the known value cot(π/3)=1/√(,3)

cot(π/3)=√(,3)/3

5. Substitute the value back into the expression from step 1.

−cot((4*π)/3)=−√(,3)/3

Final Answer

cot(−(4*π)/3)=−√(,3)/3

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