Simplify cot((7pi)/6)

Problem

cot((7*π)/6)

Solution

1. Identify the quadrant of the angle (7*π)/6 Since π<(7*π)/6<(3*π)/2 the angle is in the third quadrant.

2. Determine the reference angle. The reference angle (θ_r*e*ƒ) for an angle in the third quadrant is θ−π

(θ_r*e*ƒ)=(7*π)/6−π=π/6

3. Apply the sign of the cotangent function in the third quadrant. In the third quadrant, cotangent is positive.

cot((7*π)/6)=cot(π/6)

4. Evaluate the cotangent of the reference angle using the definition cot(θ)=cos(θ)/sin(θ)

cos(π/6)=√(,3)/2

sin(π/6)=1/2

cot(π/6)=√(,3)/2/1/2=√(,3)

Final Answer

cot((7*π)/6)=√(,3)

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