Find the Exact Value cot((23pi)/6)

Problem

cot((23*π)/6)

Solution

1. Find the coterminal angle by subtracting 2*π (which is (12*π)/6 from the given angle until it is within the standard range [0,2*π)

(23*π)/6−(12*π)/6=(11*π)/6

2. Identify the quadrant for the angle (11*π)/6 Since (3*π)/2<(11*π)/6<2*π the angle is in Quadrant IV.

3. Determine the reference angle for (11*π)/6 in Quadrant IV.

2*π−(11*π)/6=π/6

4. Apply the cotangent definition using the reference angle. In Quadrant IV, the cotangent function is negative.

cot((11*π)/6)=−cot(π/6)

5. Evaluate the exact value of cot(π/6)

cot(π/6)=√(,3)

6. Combine the results to find the final value.

cot((23*π)/6)=−√(,3)

Final Answer

cot((23*π)/6)=−√(,3)

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