Find the Exact Value cot(135 degrees )

Problem

cot(135)

Solution

1. Identify the reference angle by finding the difference between 135 and the nearest x-axis boundary, which is 180

180−135=45

2. Determine the quadrant of the angle. Since 135 is between 90 and 180 it lies in Quadrant II.

3. Apply the sign rule for the cotangent function. In Quadrant II, the cotangent function is negative.

cot(135)=−cot(45)

4. Evaluate the cotangent of the reference angle using the known value for 45

cot(45)=1

5. Combine the sign and the value to find the final result.

cot(135)=−1

Final Answer

cot(135)=−1

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