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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