How do you evaluate $cot (\frac{11 π}{6})$ $cot((11pi)/6)$ ?

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How do you evaluate $cot (\frac{11 π}{6})$ $cot((11pi)/6)$ ?

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Answer 1 · 2016-09-25T15:46:33

$\frac{cot (11 π)}{6} = - \sqrt{3}$ $cot(11pi)/6 = -sqrt3$

Explanation:

$cot (\frac{11 π}{6})$ $cot((11pi)/6)$

Recall the identity $cot θ = \frac{cos θ}{sin θ}$ $cottheta=costheta/sintheta$

Using the unit circle, $cos (\frac{11 π}{6}) = \frac{\sqrt{3}}{2}$ $cos((11pi)/6)=sqrt3/2$ and $sin (\frac{11 π}{6}) = - \frac{1}{2}$ $sin((11pi)/6)=-1/2$

$cot (\frac{11 π}{6}) = \frac{\frac{\sqrt{3}}{2}}{- \frac{1}{2}} = \frac{\sqrt{3}}{2} \cdot - \frac{2}{1} = - \sqrt{3}$ $cot((11pi)/6)=frac{sqrt3/2}{-1/2}=sqrt3/2 * -2/1=-sqrt3$

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How do you evaluate $cot (\frac{11 π}{6})$ $cot((11pi)/6)$ ?

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How do you evaluate $cot (\frac{11 π}{6})$ $cot((11pi)/6)$ ?