Find the Exact Value cot(-135 degrees )

Problem

cot(−135)

Solution

1. Use the odd-even property of the cotangent function, which states that cot(−θ)=−cot(θ)

cot(−135)=−cot(135)

2. Identify the reference angle for 135 Since 135 is in the second quadrant, the reference angle is 180−135=45

(θ_ref)=45

3. Determine the sign of the cotangent function in the second quadrant. In the second quadrant, cotangent is negative.

cot(135)=−cot(45)

4. Substitute the known value for cot(45) which is 1

cot(45)=1

5. Combine the results to find the final value.

cot(−135)=−(−cot(45))

cot(−135)=−(−1)

cot(−135)=1

Final Answer

cot(−135)=1

Want more problems? Check here!