Find the Exact Value 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′ is calculated as (7*π)/6−π

θ′=π/6

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

cot((7*π)/6)=cot(π/6)

4. Evaluate the cotangent of the reference angle using the ratio of cosine to sine.

cot(π/6)=cos(π/6)/sin(π/6)

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

cot(π/6)=√(,3)/2/1/2

6. Simplify the fraction by canceling the denominators.

cot(π/6)=√(,3)

Final Answer

cot((7*π)/6)=√(,3)

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