Find the Exact Value cot((-pi)/4)

Problem

cot(−π/4)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Apply the odd-even identities for trigonometric functions, where cos(−x)=cos(x) and sin(−x)=−sin(x)

cot(−π/4)=cos(−π/4)/sin(−π/4)

cot(−π/4)=cos(π/4)/(−sin(π/4))

3. Substitute the known values for the sine and cosine of π/4 from the unit circle.

cos(π/4)=√(,2)/2

sin(π/4)=√(,2)/2

4. Simplify the resulting fraction.

cot(−π/4)=√(,2)/2/(−√(,2)/2)

cot(−π/4)=−1

Final Answer

cot(−π/4)=−1

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