Find the Exact Value cot(pi/2)

Problem

cot(π/2)

Solution

1. Identify the trigonometric identity for the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle θ=π/2 into the identity.

cot(π/2)=cos(π/2)/sin(π/2)

3. Determine the exact values of the cosine and sine functions at π/2 using the unit circle.

cos(π/2)=0

sin(π/2)=1

4. Simplify the fraction by dividing the values.

cot(π/2)=0/1

cot(π/2)=0

Final Answer

cot(π/2)=0

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