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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