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. Substitute the given angle θ=π/4 into the expression.

cot(π/4)=cos(π/4)/sin(π/4)

3. Recall the exact values for sine and cosine at π/4 from the unit circle.

cos(π/4)=√(,2)/2

sin(π/4)=√(,2)/2

4. Simplify the fraction by dividing the identical values.

cot(π/4)=√(,2)/2/√(,2)/2

cot(π/4)=1

Final Answer

cot(π/4)=1

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