Find the Exact Value cot(pi/3)

Problem

cot(π/3)

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/3 into the identity.

cot(π/3)=cos(π/3)/sin(π/3)

3. Evaluate the exact values of the cosine and sine functions for the angle π/3 (which is 60.

cos(π/3)=1/2

sin(π/3)=√(,3)/2

4. Simplify the resulting fraction by dividing the two values.

cot(π/3)=1/2/√(,3)/2

cot(π/3)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and the denominator by √(,3)

cot(π/3)=√(,3)/3

Final Answer

cot(π/3)=√(,3)/3

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