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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