Find the Exact Value cot((37pi)/6)

Problem

cot((37*π)/6)

Solution

1. Identify the period of the cotangent function, which is π

2. Reduce the angle by subtracting multiples of the period π to find the coterminal angle within the interval [0,π)

3. Calculate the number of periods to subtract:

(37*π)/6=6*π+π/6

4. Apply the periodicity property cot(θ+n*π)=cot(θ)

cot(6*π+π/6)=cot(π/6)

5. Evaluate the cotangent of the reference angle π/6 using the ratio of cosine to sine:

cot(π/6)=cos(π/6)/sin(π/6)

6. Substitute the known values cos(π/6)=√(,3)/2 and sin(π/6)=1/2

√(,3)/2/1/2=√(,3)

Final Answer

cot((37*π)/6)=√(,3)

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