use a reference triangle in an appropriate quadrant to find the given angle. \n\n$$\\cot^{-1}\\left(\\frac{1}…

use a reference triangle in an appropriate quadrant to find the given angle. \n\n$$\\cot^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)$$\n\n$$\\cot^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)=\\square$$\n\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expre

use a reference triangle in an appropriate quadrant to find the given angle. \n\n$$\\cot^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)$$\n\n$$\\cot^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)=\\square$$\n\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expre

Answer

Explanation:

Step1: Recall the range of (y = \cot^{-1}(x))

The range of (y=\cot^{-1}(x)) is ((0,\pi)).

Step2: Use the relationship between cotangent and tangent

We know that (\cot\theta=\frac{1}{\tan\theta}). If (\cot\theta = \frac{1}{\sqrt{3}}), then (\tan\theta=\sqrt{3}).

Step3: Find the angle in the range ((0,\pi))

We know that (\tan\frac{\pi}{3}=\sqrt{3}) and (\frac{\pi}{3}\in(0,\pi))

Answer:

(\frac{\pi}{3})