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

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Question 149721: Find the exact value of cot(-pie/6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
cot%28-pi%2F6%29 Start with the given expression.


1%2Ftan%28-pi%2F6%29 Rewrite the cotangent in terms of tangent.


1%2F%28-tan%28pi%2F6%29%29 Use the identity tan%28-u%29=-tan%28u%29 to rewrite the expression.


-1%2Ftan%28pi%2F6%29 Reduce.


-1%2F%28%28sin%28pi%2F6%29%29%2F%28cos%28pi%2F6%29%29%29 Rewrite the tangent function in terms of sine and cosine.


-1%28cos%28pi%2F6%29%2Fsin%28pi%2F6%29%29 Multiply -1 by the reciprocal of the dividing fraction.


-cos%28pi%2F6%29%2Fsin%28pi%2F6%29 Multiply.



Now, let's reference the unit circle




From the unit circle, we can see that at the angle pi%2F6, there is a point on the unit circle . So this tells us that cos%28pi%2F6%29=sqrt%283%29%2F2 and sin%28pi%2F6%29=1%2F2



So this means that -cos%28pi%2F6%29%2Fsin%28pi%2F6%29 then becomes -%28sqrt%283%29%2F2%29%2F%281%2F2%29


-%28sqrt%283%29%2F2%29%2A%282%2F1%29 Multiply the first fraction by the reciprocal of the second fraction.


-%28sqrt%283%29%2Fcross%282%29%29%2A%28cross%282%29%2F1%29 Cancel like terms.


-sqrt%283%29 Multiply and simplify.


So cot%28-pi%2F6%29=-sqrt%283%29