Find the Exact Value cot(870)

Problem

cot(870^∘)

Solution

1. Find the coterminal angle by subtracting multiples of 360^∘ until the angle is between 0^∘ and 360^∘

870^∘−2*(360^∘)=870^∘−720^∘

870^∘−720^∘=150^∘

2. Identify the quadrant for 150^∘ Since 90^∘<150^∘<180^∘ the angle lies in Quadrant II.

3. Determine the reference angle for 150^∘ in Quadrant II.

180^∘−150^∘=30^∘

4. Apply the cotangent function to the reference angle and determine the sign. In Quadrant II, cotangent is negative.

cot(150^∘)=−cot(30^∘)

5. Substitute the known value for cot(30^∘) which is √(,3)

−cot(30^∘)=−√(,3)

Final Answer

cot(870^∘)=−√(,3)

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