SOLUTION: Find the exact value of cot(-pie/6)

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Start with the given expression.


Rewrite the cotangent in terms of tangent.


Use the identity to rewrite the expression.


Reduce.


Rewrite the tangent function in terms of sine and cosine.


Multiply -1 by the reciprocal of the dividing fraction.


Multiply.



Now, let's reference the unit circle




From the unit circle, we can see that at the angle , there is a point on the unit circle . So this tells us that and



So this means that then becomes


Multiply the first fraction by the reciprocal of the second fraction.


Cancel like terms.


Multiply and simplify.


So