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

Problem

cot(−(11*π)/6)

Solution

1. Find a coterminal angle by adding 2*π to the negative angle to locate its position within the first rotation of the unit circle.

θ=−(11*π)/6+2*π

θ=−(11*π)/6+(12*π)/6

θ=π/6

2. Identify the coordinates on the unit circle for the angle π/6

x=cos(π/6)=√(,3)/2

y=sin(π/6)=1/2

3. Apply the definition of the cotangent function, which is the ratio of the x-coordinate to the y-coordinate.

cot(θ)=cos(θ)/sin(θ)

cot(π/6)=√(,3)/2/1/2

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

cot(π/6)=√(,3)/2⋅2/1

cot(π/6)=√(,3)

Final Answer

cot(−(11*π)/6)=√(,3)

Want more problems? Check here!