Question

One branch of cos^–1 other than the principal value branch corresponds to ______.

Options

• `[pi/2, (3pi)/2]`

• `[pi, 2pi]- {(3pi)/2}`

• (0, π)

• [2π, 3π]

Answer 1

One branch of cos^–1 other than the principal value branch corresponds to [2π, 3π].

Explanation:

The principal value branch of the inverse cosine function, y = cos^–1(x), is defined in the interval [0, π].

The cosine function is periodic with a period of 2π. To make it a one-to-one function (so its inverse can exist), we restrict its domain to intervals of length π where the function strictly decreases or increases.

The other branches of cos^–1(x) are obtained by shifting the principal branch by multiples of π or 2π.