Find the Exact Value cot(-120 degrees )

Problem

cot(−120)

Solution

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

cot(−120)=−cot(120)

2. Identify the reference angle for 120 Since 120 is in the second quadrant, the reference angle is 180−120=60

(θ_ref)=60

3. Determine the sign of the cotangent function in the second quadrant. In Quadrant II, cosine is negative and sine is positive, so cotangent is negative.

cot(120)=−cot(60)

4. Substitute this back into the expression from step 1.

−cot(120)=−(−cot(60))

cot(−120)=cot(60)

5. Evaluate the cotangent of the reference angle using the known value cot(60)=1/√(,3)

cot(60)=√(,3)/3

Final Answer

cot(−120)=√(,3)/3

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