Question

Which interval expresses the fixed interval used to select the principal value of \[\cot^{-1}x\]?

Options

• \[\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\]

• \[[0,\pi]\]

• \[(0,\pi)\]

• \[\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\]

Answer 1

Principal value means the standard angle selected from a fixed interval. For \[\cot^{-1}x\], that interval is \[(0,\pi)\], excluding both endpoints.