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

Want more problems? Check here!