Find the Exact Value cot(-240 degrees )

Problem

cot(−240)

Solution

1. Find the coterminal angle by adding 360 to the given angle to find an equivalent angle within the standard range of 0 to 360

−240+360=120

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

3. Determine the reference angle for an angle in Quadrant II by subtracting the angle from 180

180−120=60

4. Apply the trigonometric identity for the cotangent function. In Quadrant II, cotangent is negative.

cot(120)=−cot(60)

5. Substitute the known value for cot(60) which is 1/√(,3) or √(,3)/3

cot(60)=√(,3)/3

6. Combine the results to find the final value.

cot(−240)=−√(,3)/3

Final Answer

cot(−240)=−√(,3)/3

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