Find the Exact Value cot(480)

Problem

cot(480^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from 480^∘ to bring the angle within the standard range of 0^∘ to 360^∘

480^∘−360^∘=120^∘

2. Identify the quadrant for 120^∘ Since 90^∘<120^∘<180^∘ the angle lies in Quadrant II.

3. Determine the reference angle for 120^∘ in Quadrant II by subtracting the angle from 180^∘

180^∘−120^∘=60^∘

4. Apply the trigonometric sign for the cotangent function in Quadrant II. In Quadrant II, cot(θ) is negative.

cot(120^∘)=−cot(60^∘)

5. Evaluate the exact value using the known value for cot(60^∘)=√(,3)/3

−cot(60^∘)=−√(,3)/3

Final Answer

cot(480^∘)=−√(,3)/3

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