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

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