Find the Exact Value cot(-pi/4)

Problem

cot(−π/4)

Solution

1. Identify the property of the cotangent function for negative angles. The cotangent function is odd, meaning cot(−θ)=−cot(θ)

2. Apply the odd function property to the given expression.

cot(−π/4)=−cot(π/4)

3. Recall the definition of cotangent in terms of sine and cosine.

cot(π/4)=cos(π/4)/sin(π/4)

4. Substitute the known values for sin(π/4) and cos(π/4) which are both √(,2)/2

cot(π/4)=√(,2)/2/√(,2)/2=1

5. Calculate the final result by applying the negative sign from step 2.

−1⋅1=−1

Final Answer

cot(−π/4)=−1

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