Find the Exact Value cot(-225)

Problem

cot(−225^∘)

Solution

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

cot(−225^∘)=−cot(225^∘)

2. Determine the reference angle for 225^∘ Since 225^∘ is in the third quadrant, subtract 180^∘ from the angle.

Reference Angle=225^∘−180^∘=45^∘

3. Identify the sign of the cotangent function in the third quadrant. In the third quadrant, cotangent is positive.

cot(225^∘)=cot(45^∘)

4. Evaluate the cotangent of the reference angle using the known value for 45^∘ where cot(45^∘)=1

cot(225^∘)=1

5. Substitute the value back into the expression from step 1.

−cot(225^∘)=−(1)

Final Answer

cot(−225^∘)=−1

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