Find the Exact Value cot((13pi)/6)

Problem

cot((13*π)/6)

Solution

1. Identify the angle and find its coterminal equivalent within the standard interval [0,2*π] by subtracting 2*π

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

2. Apply the definition of the cotangent function, which is the ratio of the cosine to the sine of the angle.

cot(π/6)=cos(π/6)/sin(π/6)

3. Substitute the known values for the cosine and sine of π/6 from the unit circle.

cos(π/6)=√(,3)/2

sin(π/6)=1/2

4. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

√(,3)/2/1/2=√(,3)/2⋅2/1

√(,3)/2⋅2/1=√(,3)

Final Answer

cot((13*π)/6)=√(,3)

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