Find the Exact Value cot(-pi/6)

Problem

cot(−π/6)

Solution

1. Identify the property of the cotangent function for negative angles. Since cotangent is an odd function, cot(−θ)=−cot(θ)

cot(−π/6)=−cot(π/6)

2. Express the cotangent function in terms of sine and cosine.

cot(π/6)=cos(π/6)/sin(π/6)

3. Substitute the known values for the trigonometric functions at π/6 (or 30.

cos(π/6)=√(,3)/2

sin(π/6)=1/2

4. Calculate the value of the cotangent by dividing the cosine value by the sine value.

cot(π/6)=√(,3)/2/1/2

cot(π/6)=√(,3)

5. Apply the negative sign from the first step to find the final result.

−cot(π/6)=−√(,3)

Final Answer

cot(−π/6)=−√(,3)

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