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Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______

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Q. Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
  1. Find values of cos⁡(30°)\cos(30°): Find the values of cos⁡(30°)\cos(30°) and sin⁡(30°)\sin(30°). cos⁡(30°)=3/2\cos(30°) = \sqrt{3}/2 and sin⁡(30°)=1/2\sin(30°) = 1/2.
  2. Calculate cot⁡(30°)\cot(30°): Calculate cot⁡(30°)\cot(30°) using the definition cot⁡(θ)=cos⁡(θ)sin⁡(θ)\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}. So, cot⁡(30°)=3/21/2\cot(30°) = \frac{\sqrt{3}/2}{1/2}.
  3. Simplify the fraction: Simplify the fraction by multiplying the numerator and denominator by 22. This gives us cot⁡(30°)=32×21=3\cot(30°) = \frac{\sqrt{3}}{2} \times \frac{2}{1} = \sqrt{3}.

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