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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