Find the exact value of cot 330 degrees.
Recall that the cotangent function is the reciprocal of the tangent function.
The tangent of 330 degrees can be found by evaluating the tangent of the reference angle, which is 30 degrees. However, the tangent function is negative in Quadrant IV, where 330 degrees is located.
The tangent of 30 degrees is $\sqrt{3}/3$, so the tangent of 330 degrees is $-\sqrt{3}/3$.
Therefore, the cotangent of 330 degrees is the reciprocal of $-\sqrt{3}/3$, which is $\boxed{-\sqrt{3}}$.
360 - 330 = 30 degrees below the +x axis
y axis component is -1
length of hypotenuse = 2 (because we all know sin 30 = 1/2 )
then x axis component is sqrt 3
Tan = -1 / sqrt 3
Cotan = - sqrt 3
Apologies for the incorrect explanation in the previous response.
To find the exact value of $\cot 330^\circ$, we need to first determine the reference angle.
Since $330^\circ$ is $30^\circ$ below the $+x$ axis, its reference angle is $30^\circ$. Recall that $\tan 30^\circ = \frac{\sqrt{3}}{3}$.
Since $\cot 330^\circ$ is the reciprocal of $\tan 330^\circ$, we have $\cot 330^\circ = \frac{1}{\tan 30^\circ} = \frac{1}{\frac{\sqrt{3}}{3}} = \boxed{\sqrt{3}}$.