Find the Exact Value cot(-(11pi)/6)

Problem

cot(−(11*π)/6)

Solution

1. Identify the coterminal angle within the standard interval [0,2*π) by adding 2*π to the given angle.

−(11*π)/6+2*π=−(11*π)/6+(12*π)/6

π/6

2. Apply the definition of the cotangent function in terms of sine and cosine.

cot(π/6)=cos(π/6)/sin(π/6)

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

cos(π/6)=√(,3)/2

sin(π/6)=1/2

4. Simplify the resulting fraction by multiplying by the reciprocal of the denominator.

√(,3)/2/1/2=√(,3)/2⋅2/1

√(,3)

Final Answer

cot(−(11*π)/6)=√(,3)

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