Find the Value Using the Unit Circle cot(pi/6)

Problem

cot(π/6)

Solution

1. Identify the coordinates on the unit circle for the angle θ=π/6

2. Recall that for any angle θ on the unit circle, the coordinates (x,y) are (cos(θ),sin(θ))

3. Determine the specific values for π/6 which are x=√(,3)/2 and y=1/2

4. Apply the formula for the cotangent function, which is defined as cot(θ)=cos(θ)/sin(θ) or x/y

5. Substitute the values into the formula:

cot(π/6)=√(,3)/2/1/2

6. Simplify the fraction by multiplying by the reciprocal of the denominator:

cot(π/6)=√(,3)/2⋅2/1

7. Cancel the common factor of 2 to find the final value.

Final Answer

cot(π/6)=√(,3)

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