Find the Exact Value cot((29pi)/6)

Problem

cot((29*π)/6)

Solution

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

(29*π)/6−2*((12*π)/6)=(29*π)/6−(24*π)/6

(29*π)/6−(24*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 and consider the sign in Quadrant II. In Quadrant II, cotangent is negative.

cot((5*π)/6)=−cot(π/6)

5. Evaluate the exact value using the known value for cot(π/6)=√(,3)

−cot(π/6)=−√(,3)

Final Answer

cot((29*π)/6)=−√(,3)

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