Question

give the degree measure of θ if it exists. do not use a calculator.
θ = cot⁻¹(√3)
select the correct choice below and fill in any answer boxes in your choice.
○ a. θ = □°
(type your answer in degrees.)
○ b. cot⁻¹(√3) does not exist.

Explanation:

Step1: Recall the range of the inverse cotangent function

The range of \(y = \cot^{-1}(x)\) is \((0,\pi)\) (or \((0^{\circ},180^{\circ})\) when working in degrees).

Step2: Use the cotangent identity \(\cot\theta=\frac{\cos\theta}{\sin\theta}\)

We know that \(\cot\theta=\sqrt{3}\). Also, \(\cot\theta = \frac{1}{\tan\theta}\), so if \(\cot\theta=\sqrt{3}\), then \(\tan\theta=\frac{1}{\sqrt{3}}\).
We know that \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\) and \(30^{\circ}\in(0^{\circ},180^{\circ})\)

Answer:

A. \(\theta = 30^{\circ}\)