Answer
$\dfrac{\sqrt{3}}{3}$
Work Step by Step
Convert the angle measure to degrees by multiplying $\dfrac{180^o}{\pi}$ to obtain:
$\dfrac{\pi}{3} \cdot \dfrac{180^o}{\pi} = 60^o$
RECALL:
(1) $\sin{\theta} = \dfrac{\text{opposite side}}{\text{hypotenuse}}$
(2) $\tan{\theta} = \dfrac{\text{opposite side}}{\text{adjacent side}}$
(3) $\cos{\theta} = \dfrac{\text{adjacent side}}{\text{hypotenuse}}$
(4) $\sec{\theta} = \dfrac{\text{hypotenuse}}{\text{adjacent}}$
(5) $\csc{\theta} = \dfrac{\text{hypotenuse}}{\text{opposite side}}$
(6) $\cot{\theta}=\dfrac{\text{adjacent side}}{\text{opposite side}}$
Use formula (6) above.
Use the 60-degree angle of the triangle on the right to obtain:
$\cot{\frac{\pi}{3}} = \cot{60^o} = \dfrac{1}{\sqrt3}$
Rationalize the denominator by multiplying $\sqrt3$ to both the numerator and the denominator to obtain:
$=\dfrac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}
\\=\dfrac{\sqrt{3}}{3}$
