Find the Exact Value cot(-45 degrees )

Problem

cot(−45)

Solution

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

cot(−45)=−cot(45)

2. Use the reciprocal identity to express cotangent in terms of tangent.

−cot(45)=−1/tan(45)

3. Identify the value of tan(45) from the unit circle or a special right triangle (45−45−90, where tan(45)=1

tan(45)=1

4. Substitute the value back into the expression and simplify.

−1/1=−1

Final Answer

cot(−45)=−1

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