Question

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

Explanation:

Step1: Recall the definition of inverse cotangent

The range of \(y = \cot^{-1}(x)\) is \((0^{\circ},180^{\circ})\). Also, \(\cot\theta=\frac{\cos\theta}{\sin\theta}\), and we know that \(\cot45^{\circ}=\frac{\cos45^{\circ}}{\sin45^{\circ}}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1\)

Answer:

A. \(\theta = 45^{\circ}\)