Find the Exact Value cot(-30)

Problem

cot(−30)

Solution

1. Apply the odd-even identity for the cotangent function, which states that cot(−θ)=−cot(θ)

cot(−30)=−cot(30)

2. Express the cotangent in terms of sine and cosine using the identity cot(θ)=cos(θ)/sin(θ)

−cot(30)=−cos(30)/sin(30)

3. Substitute the known values for the sine and cosine of 30 where cos(30)=√(,3)/2 and sin(30)=1/2

−cos(30)/sin(30)=−√(,3)/2/1/2

4. Simplify the fraction by multiplying the numerator by the reciprocal of the denominator.

−√(,3)/2⋅2/1=−√(,3)

Final Answer

cot(−30)=−√(,3)

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