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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