Find the Exact Value cot((17pi)/6)

Problem

cot((17*π)/6)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(17*π)/6−2*π=(17*π)/6−(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

2. Identify the quadrant for the angle (5*π)/6 Since π/2<(5*π)/6<π the angle is in Quadrant II.

3. Determine the reference angle for (5*π)/6 in Quadrant II.

π−(5*π)/6=π/6

4. Apply the cotangent definition using the reference angle and the sign for Quadrant II. In Quadrant II, cotangent is negative.

cot((5*π)/6)=−cot(π/6)

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

cot(π/6)=√(,3)

6. Combine the sign and value to find the final result.

cot((17*π)/6)=−√(,3)

Final Answer

cot((17*π)/6)=−√(,3)

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